subject:(Convex Optimization)

1. Uthayakumar, R. Study on convergence of optimization problems;.

Degree: 2014, INFLIBNET

URL: http://shodhganga.inflibnet.ac.in/handle/10603/17964

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In this thesis, various notions of convergence of sequence of sets and functions and their applications in the convergence of the optimal values under the… (more)

Subjects/Keywords: Convergence; Convex; Functions; Non-convex; Optimization; Sets

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APA (6^th Edition):

Uthayakumar, R. (2014). Study on convergence of optimization problems;. (Thesis). INFLIBNET. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/17964

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Uthayakumar, R. “Study on convergence of optimization problems;.” 2014. Thesis, INFLIBNET. Accessed October 15, 2019. http://shodhganga.inflibnet.ac.in/handle/10603/17964.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Uthayakumar, R. “Study on convergence of optimization problems;.” 2014. Web. 15 Oct 2019.

Vancouver:

Uthayakumar R. Study on convergence of optimization problems;. [Internet] [Thesis]. INFLIBNET; 2014. [cited 2019 Oct 15]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/17964.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Uthayakumar R. Study on convergence of optimization problems;. [Thesis]. INFLIBNET; 2014. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/17964

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Victoria University of Wellington

2. Jellyman, Dayle Raymond. Convex Optimization for Distributed Acoustic Beamforming.

Degree: 2017, Victoria University of Wellington

URL: http://hdl.handle.net/10063/6650

► Beamforming filter optimization can be performed over a distributed wireless sensor network, but the output calculation remains either centralized or linked in time to the… (more)

Subjects/Keywords: Distributed; Beamforming; Convex optimization

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APA (6^th Edition):

Jellyman, D. R. (2017). Convex Optimization for Distributed Acoustic Beamforming. (Masters Thesis). Victoria University of Wellington. Retrieved from http://hdl.handle.net/10063/6650

Chicago Manual of Style (16^th Edition):

Jellyman, Dayle Raymond. “Convex Optimization for Distributed Acoustic Beamforming.” 2017. Masters Thesis, Victoria University of Wellington. Accessed October 15, 2019. http://hdl.handle.net/10063/6650.

MLA Handbook (7^th Edition):

Jellyman, Dayle Raymond. “Convex Optimization for Distributed Acoustic Beamforming.” 2017. Web. 15 Oct 2019.

Vancouver:

Jellyman DR. Convex Optimization for Distributed Acoustic Beamforming. [Internet] [Masters thesis]. Victoria University of Wellington; 2017. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10063/6650.

Council of Science Editors:

Jellyman DR. Convex Optimization for Distributed Acoustic Beamforming. [Masters Thesis]. Victoria University of Wellington; 2017. Available from: http://hdl.handle.net/10063/6650

NSYSU

3. Zhang, Shu-Bin. Study on Digital Filter Design and Coefficient Quantization.

Degree: Master, Communications Engineering, 2011, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0727111-135237

► In this thesis, the basic theory is convex optimization theory[1]. And we study the problem about how to transfer to convex optimization problem from the… (more)

Subjects/Keywords: Filter; Optimization; Convex; Bits; Quantization

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APA (6^th Edition):

Zhang, S. (2011). Study on Digital Filter Design and Coefficient Quantization. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0727111-135237

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhang, Shu-Bin. “Study on Digital Filter Design and Coefficient Quantization.” 2011. Thesis, NSYSU. Accessed October 15, 2019. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0727111-135237.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhang, Shu-Bin. “Study on Digital Filter Design and Coefficient Quantization.” 2011. Web. 15 Oct 2019.

Vancouver:

Zhang S. Study on Digital Filter Design and Coefficient Quantization. [Internet] [Thesis]. NSYSU; 2011. [cited 2019 Oct 15]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0727111-135237.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhang S. Study on Digital Filter Design and Coefficient Quantization. [Thesis]. NSYSU; 2011. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0727111-135237

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Southern California

4. Taghavi, Soraya. Quantum computation and optimized error correction.

Degree: PhD, Electrical Engineering, 2010, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/308762/rec/5355

► Two subjects in the area of quantum computation are considered here. In the first chapter I present a universal model for a quantum Robot. Chapters… (more)

▼ Two subjects in the area of quantum computation are considered here. In the first chapter I present a universal model for a quantum Robot. Chapters two, three, and four are dedicated to the problem of quantum error correction/protection.; A quantum robot is described as a quantum system that moves in, and interacts with, an external environment of quantum systems. Such environments consist of arbitrary numbers and types of particles in two or three dimensional space lattices. I find a set of universal operations that enables the quantum robot to simulate arbitrary quantum dynamics.; A computational approach to the quantum error correction problem is presented in chapters two and three. I develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. This theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. I demonstrate via numerical examples that such optimized QEC procedures always achieve a higher channel fidelity than the standard error correction method, which is agnostic about the specifics of the channel. In the setting of a known noise channel the recovery ancillas are redundant for optimized quantum error correction. I show this using a general rank minimization heuristic and supporting numerical calculations. Therefore, one can further improve the fidelity by utilizing all the available ancillas in the encoding block.; However, this conclusion breaks down in the presence of an initial entanglement between the encoding and recovery ancillas. Such entanglement assisted error correction procedures are studied in chapter three. I show how entanglement can increase fidelity in the optimized setting by improving the function of the recovery ancillas.; In the last chapter quantum error protection methods, decoherence-free subspaces and subsystems, are studied in the framework of linear maps. This framework provides the most general description of open quantum system dynamics. Advisors/Committee Members: Lidar, Daniel A. (Committee Chair), Brun, Todd A. (Committee Member), Haas, Stephan (Committee Member).

Subjects/Keywords: quantum error correction; convex optimization

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APA (6^th Edition):

Taghavi, S. (2010). Quantum computation and optimized error correction. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/308762/rec/5355

Chicago Manual of Style (16^th Edition):

Taghavi, Soraya. “Quantum computation and optimized error correction.” 2010. Doctoral Dissertation, University of Southern California. Accessed October 15, 2019. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/308762/rec/5355.

MLA Handbook (7^th Edition):

Taghavi, Soraya. “Quantum computation and optimized error correction.” 2010. Web. 15 Oct 2019.

Vancouver:

Taghavi S. Quantum computation and optimized error correction. [Internet] [Doctoral dissertation]. University of Southern California; 2010. [cited 2019 Oct 15]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/308762/rec/5355.

Council of Science Editors:

Taghavi S. Quantum computation and optimized error correction. [Doctoral Dissertation]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/308762/rec/5355

Université Catholique de Louvain

5. Martin, Benoît. Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization.

Degree: 2018, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/214246

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Autonomous microgrid planning requires to consider both investments in network and generation assets as there is no connection to another power system. In this problem,… (more)

Subjects/Keywords: Planning; Microgrid; Convex optimization

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APA (6^th Edition):

Martin, B. (2018). Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/214246

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Martin, Benoît. “Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization.” 2018. Thesis, Université Catholique de Louvain. Accessed October 15, 2019. http://hdl.handle.net/2078.1/214246.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Martin, Benoît. “Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization.” 2018. Web. 15 Oct 2019.

Vancouver:

Martin B. Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization. [Internet] [Thesis]. Université Catholique de Louvain; 2018. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2078.1/214246.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Martin B. Autonomous microgrids for rural electrification : joint investment planning of power generation and distribution through convex optimization. [Thesis]. Université Catholique de Louvain; 2018. Available from: http://hdl.handle.net/2078.1/214246

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

6. Cosentino, Alessandro. Quantum State Local Distinguishability via Convex Optimization.

Degree: 2015, University of Waterloo

URL: http://hdl.handle.net/10012/9572

► Entanglement and nonlocality play a fundamental role in quantum computing. To understand the interplay between these phenomena, researchers have considered the model of local operations… (more)

▼ Entanglement and nonlocality play a fundamental role in quantum computing. To understand the interplay between these phenomena, researchers have considered the model of local operations and classical communication, or LOCC for short, which is a restricted subset of all possible operations that can be performed on a multipartite quantum system. The task of distinguishing states from a set that is known a priori to all parties is one of the most basic problems among those used to test the power of LOCC protocols, and it has direct applications to quantum data hiding, secret sharing and quantum channel capacity. The focus of this thesis is on state distinguishability problems for classes of quantum operations that are more powerful than LOCC, yet more restricted than global operations, namely the classes of separable and positive-partial-transpose (PPT) measurements. We build a framework based on convex optimization (on cone programming, in particular) to study such problems. Compared to previous approaches to the problem, the method described in this thesis provides precise numerical bounds and quantitative analytic results. By combining the duality theory of cone programming with the channel-state duality, we also establish a novel connection between the state distinguishability problem and the study of positive linear maps, which is a topic of independent interest in quantum information theory. We apply our framework to several questions that were left open in previous works regarding the distinguishability of maximally entangled states and unextendable product sets. First, we exhibit small sets of orthogonal maximally entangled states in that are not perfectly distinguishable by LOCC. As a consequence of this, we show a gap between the power of PPT and separable measurements for the task of distinguishing sets consisting only of maximally entangled states. Furthermore, we prove tight bounds on the entanglement cost that is necessary to distinguish any sets of Bell states, thus showing that quantum teleportation is optimal for this task. Finally, we provide an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements, along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements.

Subjects/Keywords: quantum information; convex optimization

1 more image…

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APA (6^th Edition):

Cosentino, A. (2015). Quantum State Local Distinguishability via Convex Optimization. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/9572

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Cosentino, Alessandro. “Quantum State Local Distinguishability via Convex Optimization.” 2015. Thesis, University of Waterloo. Accessed October 15, 2019. http://hdl.handle.net/10012/9572.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Cosentino, Alessandro. “Quantum State Local Distinguishability via Convex Optimization.” 2015. Web. 15 Oct 2019.

Vancouver:

Cosentino A. Quantum State Local Distinguishability via Convex Optimization. [Internet] [Thesis]. University of Waterloo; 2015. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10012/9572.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Cosentino A. Quantum State Local Distinguishability via Convex Optimization. [Thesis]. University of Waterloo; 2015. Available from: http://hdl.handle.net/10012/9572

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Rutgers University

7. Yao, Wang, 1985-. Approximate versions of the alternating direction method of multipliers.

Degree: PhD, Operations Research, 2016, Rutgers University

URL: https://rucore.libraries.rutgers.edu/rutgers-lib/51517/

►

Convex optimization is at the core of many of today's analysis tools for large datasets, and in particular machine learning methods. This thesis will develop… (more)

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Convex optimization is at the core of many of today's analysis tools for large datasets, and in particular machine learning methods. This thesis will develop approximate versions of the alternating directrion of multipliers (ADMM) for the general setting of minimizing the sum of two convex functions. The alternating direction method of multipliers is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problems arising from ``big data'' and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational environments. There are two fundamental approaches for proving the convergence of the ADMM, each based on a different form of two-way emph{splitting}, that is, expressing a mapping as the sum of two simpler mappings. The first approach is based on Douglas-Rachford operator splitting theory, and yields considerable insight into the convergence of the ADMM. The second convergence proof approach is at its core based on the Lagrangian splitting analysis. We present three new approximate versions of ADMM based on both convergence analyses, all of which require only knowledge of subgradients of the subproblem objectives, rather bounds on the distance to the exact subproblem solution. One version, which applies only to certain common special cases, is based on combining the operator splitting analysis of the ADMM with a relative-error proximal point algorithm of Solodov and Svaiter. A byproduct of this analysis is a new, relative-error version of the Douglas-Rachford splitting algorithm for monotone operators. The other two approximate versions of the ADMM are more general and based on the Lagrangian splitting analysis of the ADMM: one uses a summable absolute error criterion, and the other uses a relative error criterion and an auxiliary iterate sequence. We experimentally compare our new algorithms to an essentially exact form of the ADMM and to an inexact form that can be easily derived from prior theory (but again applies only to certain common special cases). These experiments show that our methods can significantly reduce total computational effort when iterative methods are used to solve ADMM subproblems.

Advisors/Committee Members: Ruszczynski, Andrzej (chair).

Subjects/Keywords: Mathematical optimization; Convex functions

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APA (6^th Edition):

Yao, Wang, 1. (2016). Approximate versions of the alternating direction method of multipliers. (Doctoral Dissertation). Rutgers University. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/51517/

Chicago Manual of Style (16^th Edition):

Yao, Wang, 1985-. “Approximate versions of the alternating direction method of multipliers.” 2016. Doctoral Dissertation, Rutgers University. Accessed October 15, 2019. https://rucore.libraries.rutgers.edu/rutgers-lib/51517/.

MLA Handbook (7^th Edition):

Yao, Wang, 1985-. “Approximate versions of the alternating direction method of multipliers.” 2016. Web. 15 Oct 2019.

Vancouver:

Yao, Wang 1. Approximate versions of the alternating direction method of multipliers. [Internet] [Doctoral dissertation]. Rutgers University; 2016. [cited 2019 Oct 15]. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/51517/.

Council of Science Editors:

Yao, Wang 1. Approximate versions of the alternating direction method of multipliers. [Doctoral Dissertation]. Rutgers University; 2016. Available from: https://rucore.libraries.rutgers.edu/rutgers-lib/51517/

University of Texas – Austin

8. Wang, Ye, Ph. D. Novel convex optimization techniques for circuit analysis and synthesis.

Degree: PhD, Electrical and Computer Engineering, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/67661

► Technology scaling brings about the need for computationally efficient methods for circuit analysis, optimization, and synthesis. Convex optimization is a special class of mathematical optimization… (more)

▼ Technology scaling brings about the need for computationally efficient methods for circuit analysis, optimization, and synthesis. Convex optimization is a special class of mathematical optimization problems which minimize convex functions over convex sets. For general optimization problems, finding a local minimum is often easier than finding a global optimal. The inherent convexity ensures that a local minimum must be a global minimum so that convex optimization problems can be solved efficiently and reliably. These techniques are widely used in the EDA community because not only many problems can inherently be modeled as convex optimization problems, but also convex approximations work well even for non-convex problems. In particular, this dissertation explores several problems in VLSI design by applying recent convex optimization techniques. This dissertation first addresses the equation-based analog synthesis which finds design parameters that achieve optimal performance with a given circuit topology. The problem of analog synthesis in deep submicron technology is that convex modeling of circuit performance functions is not accurate enough while non-convex models are generally hard to solve. This dissertation proposes two techniques to solving this problem by leveraging the recent advances in semidefinite programming problem (SDP) relaxation of polynomial optimization. The first technique addresses the computational intractability of SDP relaxation in polynomial optimization formulation. Modeling analog performance functions via general polynomials allows for highly accurate fitting of SPICE data due to their inherent non-convexity and non-linearity. However, the computational complexity of solving the corresponding SDP relaxation scales exponentially with the degree of a polynomial. This dissertation studies fitting high-degree but sparse polynomials with special structure to enable efficient subsequent optimization phase. Results demonstrate that by handling higher-degree polynomials, the fitting error can be drastically reduced, which translates to a significant increase in the rate of constraint satisfaction. The second technique addresses the main challenge of using geometric programming (GP): the mismatch between what GP can accurately fit and the behavior of true analog performance functions. This approach proposes fitting device models as high-order monomials, defined as the exponential functions of polynomials in the logarithmic variables. The introduction of high-order monomials allows significant improvements in model accuracy. Using SDP-relaxations, the proposed strategy is able to obtain efficient near-optimal global solutions. Next, this dissertation focuses on computational improvements in power grid reduction. Analysis and simulation of power grids for large integrated circuits is computationally expensive due to the tremendous number of elements in power grids. The goal of power grid reduction is to produce a sparse approximation of the original grid with… Advisors/Committee Members: Orshansky, Michael (advisor), Caramanis, Constantine (advisor), Sun, Nan (committee member), Swartzlander, Earl (committee member), Zeng, Zhiyu (committee member).

Subjects/Keywords: Convex optimization; EDA problems

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APA (6^th Edition):

Wang, Ye, P. D. (2018). Novel convex optimization techniques for circuit analysis and synthesis. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/67661

Chicago Manual of Style (16^th Edition):

Wang, Ye, Ph D. “Novel convex optimization techniques for circuit analysis and synthesis.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed October 15, 2019. http://hdl.handle.net/2152/67661.

MLA Handbook (7^th Edition):

Wang, Ye, Ph D. “Novel convex optimization techniques for circuit analysis and synthesis.” 2018. Web. 15 Oct 2019.

Vancouver:

Wang, Ye PD. Novel convex optimization techniques for circuit analysis and synthesis. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2152/67661.

Council of Science Editors:

Wang, Ye PD. Novel convex optimization techniques for circuit analysis and synthesis. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/67661

University of Texas – Austin

9. Berning, Andrew Walter, Jr. Verification of successive convexification algorithm.

Degree: MSin Engineering, Aerospace engineering, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/41579

► In this report, I describe a technique which allows a non-convex optimal control problem to be expressed and solved in a convex manner. I then… (more)

Subjects/Keywords: Convex; Convexification; Optimization; Verification

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APA (6^th Edition):

Berning, Andrew Walter, J. (2016). Verification of successive convexification algorithm. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/41579

Chicago Manual of Style (16^th Edition):

Berning, Andrew Walter, Jr. “Verification of successive convexification algorithm.” 2016. Masters Thesis, University of Texas – Austin. Accessed October 15, 2019. http://hdl.handle.net/2152/41579.

MLA Handbook (7^th Edition):

Berning, Andrew Walter, Jr. “Verification of successive convexification algorithm.” 2016. Web. 15 Oct 2019.

Vancouver:

Berning, Andrew Walter J. Verification of successive convexification algorithm. [Internet] [Masters thesis]. University of Texas – Austin; 2016. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2152/41579.

Council of Science Editors:

Berning, Andrew Walter J. Verification of successive convexification algorithm. [Masters Thesis]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/41579

Princeton University

10. Ma, Tengyu. Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding .

Degree: PhD, 2017, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01th83m199d

► Non-convex optimization is ubiquitous in modern machine learning: recent breakthroughs in deep learning require optimizing non-convex training objective functions; problems that admit accurate convex relaxation… (more)

▼ Non-convex optimization is ubiquitous in modern machine learning: recent breakthroughs in deep learning require optimizing non-convex training objective functions; problems that admit accurate convex relaxation can often be solved more efficiently with non-convex formulations. However, the theoretical understanding of non-convex optimization remained rather limited. Can we extend the algorithmic frontier by efficiently optimizing a family of interesting non-convex functions? Can we successfully apply non-convex optimization to machine learning problems with provable guarantees? How do we interpret the complicated models in machine learning that demand non-convex optimizers? Towards addressing these questions, in this thesis, we theoretically studied various machine learning models including sparse coding, topic models, and matrix completion, linear dynamical systems, and word embeddings. We first consider how to find a coarse solution to serve as a good starting point for local improvement algorithms such as stochastic gradient descent. We propose efficient methods for sparse coding and topic inference with better provable guarantees. Second, we propose a framework for analyzing local improvement algorithms that start from a course solution. We apply it successfully to the sparse coding problem. Then, we consider a family of non-convex functions satisfying that all local minima are also global (and some additional regularity property). Such functions can be optimized by local improvement algorithms efficiently from a random or arbitrary starting point. The challenge that we address here, in turn, becomes proving that an objective function belongs to this class. We establish such results for the natural learning objectives of matrix completion and linear dynamical systems. Finally, we make steps towards interpreting the non-linear models that require non-convex training algorithms. We reflect on the principles of word embeddings in natural language processing. We give a generative model for the texts, using which we explain why different non-convex formulations such as word2vec and GloVe can learn similar word embeddings with the surprising performance – analogous words have embeddings with similar differences. Advisors/Committee Members: Arora, Sanjeev (advisor).

Subjects/Keywords: machine learning; non-convex optimization

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APA (6^th Edition):

Ma, T. (2017). Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01th83m199d

Chicago Manual of Style (16^th Edition):

Ma, Tengyu. “Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding .” 2017. Doctoral Dissertation, Princeton University. Accessed October 15, 2019. http://arks.princeton.edu/ark:/88435/dsp01th83m199d.

MLA Handbook (7^th Edition):

Ma, Tengyu. “Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding .” 2017. Web. 15 Oct 2019.

Vancouver:

Ma T. Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding . [Internet] [Doctoral dissertation]. Princeton University; 2017. [cited 2019 Oct 15]. Available from: http://arks.princeton.edu/ark:/88435/dsp01th83m199d.

Council of Science Editors:

Ma T. Non-convex Optimization for Machine Learning: Design, Analysis, and Understanding . [Doctoral Dissertation]. Princeton University; 2017. Available from: http://arks.princeton.edu/ark:/88435/dsp01th83m199d

University of Ontario Institute of Technology

11. Takeva-Velkova, Viliyana. Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI).

Degree: 2010, University of Ontario Institute of Technology

URL: http://hdl.handle.net/10155/104

► Magnetic Resonance Imaging (MRI) is an essential instrument in clinical diag- nosis; however, it is burdened by a slow data acquisition process due to physical… (more)

Subjects/Keywords: Compressive sensing; Sparse MRI; Convex optimization

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APA (6^th Edition):

Takeva-Velkova, V. (2010). Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI). (Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/104

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Takeva-Velkova, Viliyana. “Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI).” 2010. Thesis, University of Ontario Institute of Technology. Accessed October 15, 2019. http://hdl.handle.net/10155/104.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Takeva-Velkova, Viliyana. “Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI).” 2010. Web. 15 Oct 2019.

Vancouver:

Takeva-Velkova V. Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI). [Internet] [Thesis]. University of Ontario Institute of Technology; 2010. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10155/104.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Takeva-Velkova V. Optimization algorithms in compressive sensing (CS) sparse magnetic resonance imaging (MRI). [Thesis]. University of Ontario Institute of Technology; 2010. Available from: http://hdl.handle.net/10155/104

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Ghana

12. Katsekpor, T. Iterative Methods for Large Scale Convex Optimization .

Degree: 2017, University of Ghana

URL: http://ugspace.ug.edu.gh/handle/123456789/23393

► This thesis presents a detailed description and analysis of Bregman’s iterative method for convex programming with linear constraints. Row and block action methods for large… (more)

Subjects/Keywords: Iterative Methods; Large Scale Convex; Optimization

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APA (6^th Edition):

Katsekpor, T. (2017). Iterative Methods for Large Scale Convex Optimization . (Doctoral Dissertation). University of Ghana. Retrieved from http://ugspace.ug.edu.gh/handle/123456789/23393

Chicago Manual of Style (16^th Edition):

Katsekpor, T. “Iterative Methods for Large Scale Convex Optimization .” 2017. Doctoral Dissertation, University of Ghana. Accessed October 15, 2019. http://ugspace.ug.edu.gh/handle/123456789/23393.

MLA Handbook (7^th Edition):

Katsekpor, T. “Iterative Methods for Large Scale Convex Optimization .” 2017. Web. 15 Oct 2019.

Vancouver:

Katsekpor T. Iterative Methods for Large Scale Convex Optimization . [Internet] [Doctoral dissertation]. University of Ghana; 2017. [cited 2019 Oct 15]. Available from: http://ugspace.ug.edu.gh/handle/123456789/23393.

Council of Science Editors:

Katsekpor T. Iterative Methods for Large Scale Convex Optimization . [Doctoral Dissertation]. University of Ghana; 2017. Available from: http://ugspace.ug.edu.gh/handle/123456789/23393

Universidade Nova

13. Soares, Diogo Lopes. Design of multidimensional compact constellations with high power efficiency.

Degree: 2013, Universidade Nova

URL: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11111

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia Advisors/Committee Members: Dinis, Rui, Beko, Marko.

Subjects/Keywords: Multidimensional constellations; Power efficiency; Convex optimization

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APA (6^th Edition):

Soares, D. L. (2013). Design of multidimensional compact constellations with high power efficiency. (Thesis). Universidade Nova. Retrieved from http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11111

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Soares, Diogo Lopes. “Design of multidimensional compact constellations with high power efficiency.” 2013. Thesis, Universidade Nova. Accessed October 15, 2019. http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11111.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Soares, Diogo Lopes. “Design of multidimensional compact constellations with high power efficiency.” 2013. Web. 15 Oct 2019.

Vancouver:

Soares DL. Design of multidimensional compact constellations with high power efficiency. [Internet] [Thesis]. Universidade Nova; 2013. [cited 2019 Oct 15]. Available from: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11111.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Soares DL. Design of multidimensional compact constellations with high power efficiency. [Thesis]. Universidade Nova; 2013. Available from: http://www.rcaap.pt/detail.jsp?id=oai:run.unl.pt:10362/11111

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Delft University of Technology

14. Zhang, H.M. Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:.

Degree: 2015, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:932db0bb-da4c-4ffe-892a-036d01a8071b

► The Primal-Dual Method of Multipliers (PDMM) is a new algorithm that solves convex optimization problems in a distributed manner. This study focuses on the convergence… (more)

Subjects/Keywords: convex optimization; distributed signal processing; ADMM; PDMM

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APA (6^th Edition):

Zhang, H. M. (2015). Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:932db0bb-da4c-4ffe-892a-036d01a8071b

Chicago Manual of Style (16^th Edition):

Zhang, H M. “Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:.” 2015. Masters Thesis, Delft University of Technology. Accessed October 15, 2019. http://resolver.tudelft.nl/uuid:932db0bb-da4c-4ffe-892a-036d01a8071b.

MLA Handbook (7^th Edition):

Zhang, H M. “Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:.” 2015. Web. 15 Oct 2019.

Vancouver:

Zhang HM. Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:. [Internet] [Masters thesis]. Delft University of Technology; 2015. [cited 2019 Oct 15]. Available from: http://resolver.tudelft.nl/uuid:932db0bb-da4c-4ffe-892a-036d01a8071b.

Council of Science Editors:

Zhang HM. Distributed Convex Optimization: A Study on the Primal-Dual Method of Multipliers:. [Masters Thesis]. Delft University of Technology; 2015. Available from: http://resolver.tudelft.nl/uuid:932db0bb-da4c-4ffe-892a-036d01a8071b

Iowa State University

15. Li, Chong. Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds.

Degree: 2013, Iowa State University

URL: https://lib.dr.iastate.edu/etd/13421

► Since the success of obtaining the capacity (i.e. the maximal achievable transmission rate under which the message can be recovered with arbitrarily small probability of… (more)

▼ Since the success of obtaining the capacity (i.e. the maximal achievable transmission rate under which the message can be recovered with arbitrarily small probability of error) for non-feedback point-to-point communication channels by C. Shannon (in 1948), Information Theory has been proved to be a powerful tool to derive fundamental limitations in communication systems. During the last decade, motivated by the emerging of networked systems, information theorists have turned lots of their attention to communication channels with feedback (through another channel from receiver to transmitter). Under the assumption that the feedback channel is noiseless, a large body of notable results have been derived, although much work still needs to be done. However, when this ideal assumption is removed, i.e., the feedback channel is noisy, only few valuable results can be found in the literature and many challenging problems are still open. This thesis aims to address some of these long-standing noisy feedback problems, with concentration on the channel capacity. First of all, we analyze the fundamental information flow in noisy feedback channels. We introduce a new notion, the residual directed information, in order to characterize the noisy feedback channel capacity for which the standard directed information can not be used. As an illustration, finite-alphabet noisy feedback channels have been studied in details. Next, we provide an information flow decomposition equality which serves as a foundation of other novel results in this thesis. With the result of information flow decomposition in hand, we next investigate time-varying Gaussian channels with additive Gaussian noise feedback. Following the notable Cover-Pombra results in 1989, we define the n-block noisy feedback capacity and derive a pair of n-block upper and lower bounds on the n-block noisy feedback capacity. These bounds can be obtained by efficiently solving convex optimization problems. Under the assumption of stationarity on the additive Gaussian noises, we show that the limits of these n-block bounds can be characterized in a power spectral optimization form. In addition, two computable lower bounds are derived for the Shannon capacity. Next, we consider a class of channels where feedback could not increase the capacity and thus the noisy feedback capacity equals to the non-feedback capacity. We derive a necessary condition (characterized by the directed information) for the capacity-achieving channel codes. The condition implies that using noisy feedback is detrimental to achievable rate, i.e, the capacity can not be achieved by using noisy feedback. Finally, we introduce a new framework of communication channels with noisy feedback where the feedback information received by the transmitter is also available to the decoder with some finite delays. We investigate the capacity and linear coding schemes for this extended noisy feedback channels. To summarize, this thesis firstly provides a foundation (i.e. information flow analysis) for analyzing communications…

Subjects/Keywords: Capacity; Convex Optimization; Feedback; Information Theory; Engineering

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APA (6^th Edition):

Li, C. (2013). Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/13421

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Li, Chong. “Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds.” 2013. Thesis, Iowa State University. Accessed October 15, 2019. https://lib.dr.iastate.edu/etd/13421.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Li, Chong. “Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds.” 2013. Web. 15 Oct 2019.

Vancouver:

Li C. Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds. [Internet] [Thesis]. Iowa State University; 2013. [cited 2019 Oct 15]. Available from: https://lib.dr.iastate.edu/etd/13421.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Li C. Fundamental limitations on communication channels with noisy feedback: information flow, capacity and bounds. [Thesis]. Iowa State University; 2013. Available from: https://lib.dr.iastate.edu/etd/13421

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Université Catholique de Louvain

16. Orban de Xivry, François-Xavier. Nearest stable system.

Degree: 2013, Université Catholique de Louvain

URL: http://hdl.handle.net/2078.1/132586

►

Stability is a universal concept which we experience in our everyday lives. It plays a central role in the study of dynamical systems and is… (more)

Subjects/Keywords: Stability; Dynamical system; Convex optimization; Nonconvex; Nonsmooth

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APA (6^th Edition):

Orban de Xivry, F. (2013). Nearest stable system. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/132586

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Orban de Xivry, François-Xavier. “Nearest stable system.” 2013. Thesis, Université Catholique de Louvain. Accessed October 15, 2019. http://hdl.handle.net/2078.1/132586.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Orban de Xivry, François-Xavier. “Nearest stable system.” 2013. Web. 15 Oct 2019.

Vancouver:

Orban de Xivry F. Nearest stable system. [Internet] [Thesis]. Université Catholique de Louvain; 2013. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2078.1/132586.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Orban de Xivry F. Nearest stable system. [Thesis]. Université Catholique de Louvain; 2013. Available from: http://hdl.handle.net/2078.1/132586

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

17. Karimi, Mehdi. Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods.

Degree: 2017, University of Waterloo

URL: http://hdl.handle.net/10012/12209

► This thesis studies the theory and implementation of infeasible-start primal-dual interior-point methods for convex optimization problems. Convex optimization has applications in many fields of engineering… (more)

Subjects/Keywords: convex optimization; primal-dual interior-point methods

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APA (6^th Edition):

Karimi, M. (2017). Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/12209

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Karimi, Mehdi. “Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods.” 2017. Thesis, University of Waterloo. Accessed October 15, 2019. http://hdl.handle.net/10012/12209.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Karimi, Mehdi. “Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods.” 2017. Web. 15 Oct 2019.

Vancouver:

Karimi M. Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods. [Internet] [Thesis]. University of Waterloo; 2017. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10012/12209.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Karimi M. Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods. [Thesis]. University of Waterloo; 2017. Available from: http://hdl.handle.net/10012/12209

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Minnesota

18. Choi, Hyungjin. Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization.

Degree: PhD, Electrical Engineering, 2017, University of Minnesota

URL: http://hdl.handle.net/11299/190457

► Rampant integration of renewable resources (e.g., photovoltaic and wind-energy conversion systems) and uncontrollable and elastic loads (e.g., plug-in hybrid electric vehicles) are rapidly transforming power… (more)

Subjects/Keywords: Convex Optimization; Power Systems; Sensitivity; Stability; Uncertainty

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APA (6^th Edition):

Choi, H. (2017). Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/190457

Chicago Manual of Style (16^th Edition):

Choi, Hyungjin. “Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization.” 2017. Doctoral Dissertation, University of Minnesota. Accessed October 15, 2019. http://hdl.handle.net/11299/190457.

MLA Handbook (7^th Edition):

Choi, Hyungjin. “Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization.” 2017. Web. 15 Oct 2019.

Vancouver:

Choi H. Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization. [Internet] [Doctoral dissertation]. University of Minnesota; 2017. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/11299/190457.

Council of Science Editors:

Choi H. Quantication of the Impact of Uncertainty in Power Systems using Convex Optimization. [Doctoral Dissertation]. University of Minnesota; 2017. Available from: http://hdl.handle.net/11299/190457

19. Umenberger, Jack. Convex Identifcation of Stable Dynamical Systems .

Degree: 2017, University of Sydney

URL: http://hdl.handle.net/2123/17321

► This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems… (more)

▼ This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems.

Subjects/Keywords: system identification; convex optimization; positive systems

1 more image…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Umenberger, J. (2017). Convex Identifcation of Stable Dynamical Systems . (Thesis). University of Sydney. Retrieved from http://hdl.handle.net/2123/17321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Umenberger, Jack. “Convex Identifcation of Stable Dynamical Systems .” 2017. Thesis, University of Sydney. Accessed October 15, 2019. http://hdl.handle.net/2123/17321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Umenberger, Jack. “Convex Identifcation of Stable Dynamical Systems .” 2017. Web. 15 Oct 2019.

Vancouver:

Umenberger J. Convex Identifcation of Stable Dynamical Systems . [Internet] [Thesis]. University of Sydney; 2017. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2123/17321.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Umenberger J. Convex Identifcation of Stable Dynamical Systems . [Thesis]. University of Sydney; 2017. Available from: http://hdl.handle.net/2123/17321

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Tartu University

20. Makkeh, Abdullah. Applications of optimization in some complex systems .

Degree: 2018, Tartu University

URL: http://hdl.handle.net/10062/61143

► Matemaatiline optimeerimine on optimeerimisülesandele optimaalse lahendi leidmine, see tähendab, et leitakse reaalarvuliste väärtustega funktsiooni (eesmärkfunktsiooni) teatud kitsendusi rahuldav maksimaalne või minimaalne väärtus. Matemaatiline optimeerimine on… (more)

▼ Matemaatiline optimeerimine on optimeerimisülesandele optimaalse lahendi leidmine, see tähendab, et leitakse reaalarvuliste väärtustega funktsiooni (eesmärkfunktsiooni) teatud kitsendusi rahuldav maksimaalne või minimaalne väärtus. Matemaatiline optimeerimine on jagatud eesmärkfunktsiooni ja kitsenduste põhjal erinevatesse klassidesse ja need klassid erinevad arvutusliku keerukuse poolest. Praktikas on vaja nende ülesannetega toime tulemiseks robustseid ja kiireid algoritme. Optimeerimisülesanded, mis kuuluvad polünomiaalse keerukusega klassi saab lahendada otseselt. Erinevate optimeerimisülesannete lahendamiseks on olemas algoritmid, eelkõige polünomiaalse keerukusega klassi jaoks. Mõnedel juhtudel pole isegi efektiivsed algoritmid ülesande lahendamiseks piisavalt head, näiteks liiga aeglased. Nendel juhtudel saab optimeerimisprotsessi uurimise abil kindlaks teha probleemi põhjused ja muuta algoritmi selliselt, et neid vältida. Antud töö uurib kumera optimeerimisülesande (Convex Program) lahendust, mille abil on võimalik saavutada osaline informatsiooni liigendamine (partial information decomposition) ning hiljuti kasutati seda teatava keerulise süsteemi analüüsimiseks. Kumerate optimeerimisülesannete lahendamisel tekkivate probleemidega toime tulemiseks loodi antud töös kiire ja robustne algoritm. Lisaks uuritakse antud töös situatsiooni, mis tuli hiljuti esile neuroteaduse valdkonnas, kus osaline informatsiooni liigendamise ülesanne lahendatakse kitsendustega. Viimasena uuritakse antud töös optimeerimisülesannet automatiseeritud süsteemi juhtimiseks, mis on APX keerukusega. Ülesanne modelleeritakse täisarvulise planeerimise ja kehtestatavuse kontrollimise mudelitena, mida saab edaspidi kasutada heuristikute loomiseks, et lahendada ülesanne mõistliku ajaga.; Mathematical Optimization is finding the optimal solution to an optimization problem, i.e., the maximum or minimum value of a real function (objective function) subjected to a set of constraints. Mathematical optimization is divided into classes depending on the nature of the objective function as well as the constraints and these classes vary in their computational complexity. In practice, robust and fast processes are needed to tackle the problems, and so optimization problems which can be modeled into classes of polynomial complexity are applied directly. Several algorithms that solve different optimization problems exist, in particular, efficient ones for the classes with polynomial complexity. But, in some cases, even the efficient algorithms face difficulties in solving optimization problems such as taking immensely long time to find the optimal solution. In this case, studying the optimization, in-depth, leads to the reasons behind these pitfalls and thus modify the algorithms to avoid them. This thesis studies the solution of a Convex Program which was used to obtain partial information decomposition, a tool used recently to analyze particular complex systems. Many difficulties arise in solving the Convex Program and so the study done in this thesis… Advisors/Committee Members: Theis, Dirk Oliver, juhendaja (advisor).

Subjects/Keywords: complex systems; optimization; convex sets; software

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APA (6^th Edition):

Makkeh, A. (2018). Applications of optimization in some complex systems . (Thesis). Tartu University. Retrieved from http://hdl.handle.net/10062/61143

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Makkeh, Abdullah. “Applications of optimization in some complex systems .” 2018. Thesis, Tartu University. Accessed October 15, 2019. http://hdl.handle.net/10062/61143.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Makkeh, Abdullah. “Applications of optimization in some complex systems .” 2018. Web. 15 Oct 2019.

Vancouver:

Makkeh A. Applications of optimization in some complex systems . [Internet] [Thesis]. Tartu University; 2018. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10062/61143.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Makkeh A. Applications of optimization in some complex systems . [Thesis]. Tartu University; 2018. Available from: http://hdl.handle.net/10062/61143

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Loughborough University

21. Rossetti, Gaia. Mathematical optimization techniques for cognitive radar networks.

Degree: PhD, 2018, Loughborough University

URL: https://dspace.lboro.ac.uk/2134/33419 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747937

► This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from… (more)

▼ This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities…

Subjects/Keywords: Waveform optimization; Convex optimization; Robust optimization; Cognitive radars

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rossetti, G. (2018). Mathematical optimization techniques for cognitive radar networks. (Doctoral Dissertation). Loughborough University. Retrieved from https://dspace.lboro.ac.uk/2134/33419 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747937

Chicago Manual of Style (16^th Edition):

Rossetti, Gaia. “Mathematical optimization techniques for cognitive radar networks.” 2018. Doctoral Dissertation, Loughborough University. Accessed October 15, 2019. https://dspace.lboro.ac.uk/2134/33419 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747937.

MLA Handbook (7^th Edition):

Rossetti, Gaia. “Mathematical optimization techniques for cognitive radar networks.” 2018. Web. 15 Oct 2019.

Vancouver:

Rossetti G. Mathematical optimization techniques for cognitive radar networks. [Internet] [Doctoral dissertation]. Loughborough University; 2018. [cited 2019 Oct 15]. Available from: https://dspace.lboro.ac.uk/2134/33419 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747937.

Council of Science Editors:

Rossetti G. Mathematical optimization techniques for cognitive radar networks. [Doctoral Dissertation]. Loughborough University; 2018. Available from: https://dspace.lboro.ac.uk/2134/33419 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.747937

University of Waterloo

22. Linhares Rodrigues, Andre. Approximation Algorithms for Distributionally Robust Stochastic Optimization.

Degree: 2019, University of Waterloo

URL: http://hdl.handle.net/10012/14639

► Two-stage stochastic optimization is a widely used framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios,… (more)

▼ Two-stage stochastic optimization is a widely used framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we take first-stage actions knowing only the underlying distribution and before a scenario is realized, and may take additional second-stage recourse actions after a scenario is realized. The goal is typically to minimize the total expected cost. A common criticism levied at this model is that the underlying probability distribution is itself often imprecise. To address this, an approach that is quite versatile and has gained popularity in the stochastic-optimization literature is the two-stage distributionally robust stochastic model: given a collection D of probability distributions, our goal now is to minimize the maximum expected total cost with respect to a distribution in D. There has been almost no prior work however on developing approximation algorithms for distributionally robust problems where the underlying scenario collection is discrete, as is the case with discrete-optimization problems. We provide frameworks for designing approximation algorithms in such settings when the collection D is a ball around a central distribution, defined relative to two notions of distance between probability distributions: Wasserstein metrics (which include the L_1 metric) and the L_infinity metric. Our frameworks yield efficient algorithms even in settings with an exponential number of scenarios, where the central distribution may only be accessed via a sampling oracle. For distributionally robust optimization under a Wasserstein ball, we first show that one can utilize the sample average approximation (SAA) method (solve the distributionally robust problem with an empirical estimate of the central distribution) to reduce the problem to the case where the central distribution has a polynomial-size support, and is represented explicitly. This follows because we argue that a distributionally robust problem can be reduced in a novel way to a standard two-stage stochastic problem with bounded inflation factor, which enables one to use the SAA machinery developed for two-stage stochastic problems. Complementing this, we show how to approximately solve a fractional relaxation of the SAA problem (i.e., the distributionally robust problem obtained by replacing the original central distribution with its empirical estimate). Unlike in two-stage {stochastic, robust} optimization with polynomially many scenarios, this turns out to be quite challenging. We utilize a variant of the ellipsoid method for convex optimization in conjunction with several new ideas to show that the SAA problem can be approximately solved provided that we have an (approximation) algorithm for a certain max-min problem that is akin to, and generalizes, the k-max-min problem (find the worst-case scenario consisting of at most k elements) encountered in two-stage robust optimization. We obtain such an algorithm for various…

Subjects/Keywords: approximation algorithms; stochastic optimization; discrete optimization; convex optimization

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Linhares Rodrigues, A. (2019). Approximation Algorithms for Distributionally Robust Stochastic Optimization. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14639

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Linhares Rodrigues, Andre. “Approximation Algorithms for Distributionally Robust Stochastic Optimization.” 2019. Thesis, University of Waterloo. Accessed October 15, 2019. http://hdl.handle.net/10012/14639.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Linhares Rodrigues, Andre. “Approximation Algorithms for Distributionally Robust Stochastic Optimization.” 2019. Web. 15 Oct 2019.

Vancouver:

Linhares Rodrigues A. Approximation Algorithms for Distributionally Robust Stochastic Optimization. [Internet] [Thesis]. University of Waterloo; 2019. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/10012/14639.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Linhares Rodrigues A. Approximation Algorithms for Distributionally Robust Stochastic Optimization. [Thesis]. University of Waterloo; 2019. Available from: http://hdl.handle.net/10012/14639

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Loughborough University

23. Rossetti, Gaia. Mathematical optimization techniques for cognitive radar networks.

Degree: PhD, 2018, Loughborough University

URL: http://hdl.handle.net/2134/33419

► This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from… (more)

▼ This thesis discusses mathematical optimization techniques for waveform design in cognitive radars. These techniques have been designed with an increasing level of sophistication, starting from a bistatic model (i.e. two transmitters and a single receiver) and ending with a cognitive network (i.e. multiple transmitting and multiple receiving radars). The environment under investigation always features strong signal-dependent clutter and noise. All algorithms are based on an iterative waveform-filter optimization. The waveform optimization is based on convex optimization techniques and the exploitation of initial radar waveforms characterized by desired auto and cross-correlation properties. Finally, robust optimization techniques are introduced to account for the assumptions made by cognitive radars on certain second order statistics such as the covariance matrix of the clutter. More specifically, initial optimization techniques were proposed for the case of bistatic radars. By maximizing the signal to interference and noise ratio (SINR) under certain constraints on the transmitted signals, it was possible to iteratively optimize both the orthogonal transmission waveforms and the receiver filter. Subsequently, the above work was extended to a convex optimization framework for a waveform design technique for bistatic radars where both radars transmit and receive to detect targets. The method exploited prior knowledge of the environment to maximize the accumulated target return signal power while keeping the disturbance power to unity at both radar receivers. The thesis further proposes convex optimization based waveform designs for multiple input multiple output (MIMO) based cognitive radars. All radars within the system are able to both transmit and receive signals for detecting targets. The proposed model investigated two complementary optimization techniques. The first one aims at optimizing the signal to interference and noise ratio (SINR) of a specific radar while keeping the SINR of the remaining radars at desired levels. The second approach optimizes the SINR of all radars using a max-min optimization criterion. To account for possible mismatches between actual parameters and estimated ones, this thesis includes robust optimization techniques. Initially, the multistatic, signal-dependent model was tested against existing worst-case and probabilistic methods. These methods appeared to be over conservative and generic for the considered signal-dependent clutter scenario. Therefore a new approach was derived where uncertainty was assumed directly on the radar cross-section and Doppler parameters of the clutters. Approximations based on Taylor series were invoked to make the optimization problem convex and {subsequently} determine robust waveforms with specific SINR outage constraints. Finally, this thesis introduces robust optimization techniques for through-the-wall radars. These are also cognitive but rely on different optimization techniques than the ones previously discussed. By noticing the similarities…

Subjects/Keywords: Waveform optimization; Convex optimization; Robust optimization; Cognitive radars

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APA (6^th Edition):

Rossetti, G. (2018). Mathematical optimization techniques for cognitive radar networks. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/33419

Chicago Manual of Style (16^th Edition):

Rossetti, Gaia. “Mathematical optimization techniques for cognitive radar networks.” 2018. Doctoral Dissertation, Loughborough University. Accessed October 15, 2019. http://hdl.handle.net/2134/33419.

MLA Handbook (7^th Edition):

Rossetti, Gaia. “Mathematical optimization techniques for cognitive radar networks.” 2018. Web. 15 Oct 2019.

Vancouver:

Rossetti G. Mathematical optimization techniques for cognitive radar networks. [Internet] [Doctoral dissertation]. Loughborough University; 2018. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2134/33419.

Council of Science Editors:

Rossetti G. Mathematical optimization techniques for cognitive radar networks. [Doctoral Dissertation]. Loughborough University; 2018. Available from: http://hdl.handle.net/2134/33419

Georgia Tech

24. Lan, Guanghui. Convex optimization under inexact first-order information.

Degree: PhD, Industrial and Systems Engineering, 2009, Georgia Tech

URL: http://hdl.handle.net/1853/29732

► In this thesis we investigate the design and complexity analysis of the algorithms to solve convex programming problems under inexact first-order information. In the first… (more)

▼ In this thesis we investigate the design and complexity analysis of the algorithms to solve convex programming problems under inexact first-order information. In the first part of this thesis we focus on the general non-smooth convex minimization under a stochastic oracle. We start by introducing an important algorithmic advancement in this area, namely, the development of the mirror descent stochastic approximation algorithm. The main contribution is to develop a validation procedure for this algorithm applied to stochastic programming. In the second part of this thesis we consider the Stochastic Composite Optimizaiton (SCO) which covers smooth, non-smooth and stochastic convex optimization as certain special cases. Note that the optimization algorithms that can achieve this lower bound had never been developed. Our contribution in this topic mainly consists of the following aspects. Firstly, with a novel analysis, it is demonstrated that the simple RM-SA algorithm applied to the aforementioned problems exhibits the best known so far rate of convergence. Moreover, by adapting Nesterov's optimal method, we propose an accelerated SA, which can achieve, uniformly in dimension, the theoretically optimal rate of convergence for solving this class of problems. Finally, the significant advantages of the accelerated SA over the existing algorithms are illustrated in the context of solving a class of stochastic programming problems. In the last part of this work, we extend our attention to certain deterministic optimization techniques which operate on approximate first-order information for the dual problem. In particular, we establish, for the first time in the literature, the iteration-complexity for the inexact augmented Lagrangian (I-AL) methods applied to a special class of convex programming problems. Advisors/Committee Members: Arkadi Nemirovski (Committee Chair), Alexander Shapiro (Committee Co-Chair), Renato D. C. Monteiro (Committee Co-Chair), Anatoli Jouditski (Committee Member), Shabbir Ahmed (Committee Member).

Subjects/Keywords: Convex optimization; Stochastic programming; First-order methods; Uncertainty; Mathematical optimization; Convex functions; First-order logic

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Lan, G. (2009). Convex optimization under inexact first-order information. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/29732

Chicago Manual of Style (16^th Edition):

Lan, Guanghui. “Convex optimization under inexact first-order information.” 2009. Doctoral Dissertation, Georgia Tech. Accessed October 15, 2019. http://hdl.handle.net/1853/29732.

MLA Handbook (7^th Edition):

Lan, Guanghui. “Convex optimization under inexact first-order information.” 2009. Web. 15 Oct 2019.

Vancouver:

Lan G. Convex optimization under inexact first-order information. [Internet] [Doctoral dissertation]. Georgia Tech; 2009. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/1853/29732.

Council of Science Editors:

Lan G. Convex optimization under inexact first-order information. [Doctoral Dissertation]. Georgia Tech; 2009. Available from: http://hdl.handle.net/1853/29732

Penn State University

25. Kang, Bosung. Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP).

Degree: PhD, Electrical Engineering, 2015, Penn State University

URL: https://etda.libraries.psu.edu/catalog/26539

► Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP) since estimation of the disturbance or interference… (more)

▼ Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP) since estimation of the disturbance or interference covariance matrix plays a central role on radar target detection in the presence of clutter, noise and a jammer. The disturbance covariance matrix should be inferred from training sample observations in practice. Traditional maximum likelihood (ML) estimators are effective when homogeneous (target free) training data is abundant but lead to poor estimates, degraded false alarm rates, and detection loss in the regime of limited training. However, large number of homogeneous training samples are generally not available because of difficulty of guaranteeing target free disturbance observation, practical limitations imposed by the spatio-temporal nonstationarity, and system considerations. The problem has been exacerbated by recent advances that have led to more antenna elements (J) and higher temporal resolution (P) time epochs resulting in a large dimension (N = JP). In this dissertation, we look to address the aforementioned challenges by exploiting physically inspired constraints into ML estimation. While adding constraints is beneficial to achieve satisfactory performance in the practical regime of limited training, it leads to a challenging problem. Unlike unconstrained estimators, a vast majority of constrained radar STAP estimators are iterative and expensive numerically, which prohibits practical deployment. We focus on breaking this classical trade-off between computational tractability and desirable performance measures, particularly in training starved regimes. In particular, we exploit both the structure of the disturbance covariance and importantly the knowledge of the clutter rank to yield a new rank constrained maximum likelihood (RCML) estimator of clutter/disturbance covariance. We demonstrate that the rank-constrained estimation problem can in fact be cast in the framework of a tractable convex optimization problem, and derive closed form expressions for the estimated covariance matrix. In addition, we derive a new covariance estimator for STAP that jointly considers a Toeplitz structure and a rank constraint on the clutter component. Past work has shown that in the regime of low training, even handling each constraint individually is hard and techniques often resort to slow numerically based solutions. Our proposed solution leverages the rank constrained ML estimator (RCML) of structured covariances to build a computationally friendly approximation that involves a cascade of two closed form solutions. Performance analysis using the KASSPER data set (where ground truth covariance is made available) shows that the proposed RCML estimator vastly outperforms state-of-the art alternatives even for low training including the notoriously difficult regime of K <= N training regimes and for the experiments considering real-world scenarios such as target detection performance and the case that some of training samples are corrupted…

Subjects/Keywords: convex optimization; STAP; radar signal processing; constrained optimization; detection and estimation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kang, B. (2015). Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP). (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/26539

Chicago Manual of Style (16^th Edition):

Kang, Bosung. “Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP).” 2015. Doctoral Dissertation, Penn State University. Accessed October 15, 2019. https://etda.libraries.psu.edu/catalog/26539.

MLA Handbook (7^th Edition):

Kang, Bosung. “Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP).” 2015. Web. 15 Oct 2019.

Vancouver:

Kang B. Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP). [Internet] [Doctoral dissertation]. Penn State University; 2015. [cited 2019 Oct 15]. Available from: https://etda.libraries.psu.edu/catalog/26539.

Council of Science Editors:

Kang B. Robust Covariance Matrix Estimation for Radar Space-Time Adaptive Processing (STAP). [Doctoral Dissertation]. Penn State University; 2015. Available from: https://etda.libraries.psu.edu/catalog/26539

University of Oxford

26. Banjac, Goran. Operator splitting methods for convex optimization : analysis and implementation.

Degree: PhD, 2018, University of Oxford

URL: https://ora.ox.ac.uk/objects/uuid:17ac73af-9fdf-4cf6-a946-3048da3fc9c2 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740972

► Convex optimization problems are a class of mathematical problems which arise in numerous applications. Although interior-point methods can in principle solve these problems efficiently, they… (more)

▼ Convex optimization problems are a class of mathematical problems which arise in numerous applications. Although interior-point methods can in principle solve these problems efficiently, they may become intractable for solving large-scale problems or be unsuitable for real-time embedded applications. Iterations of operator splitting methods are relatively simple and computationally inexpensive, which makes them suitable for these applications. However, some of their known limitations are slow asymptotic convergence, sensitivity to ill-conditioning, and inability to detect infeasible problems. The aim of this thesis is to better understand operator splitting methods and to develop reliable software tools for convex optimization. The main analytical tool in our investigation of these methods is their characterization as the fixed-point iteration of a nonexpansive operator. The fixed-point theory of nonexpansive operators has been studied for several decades. By exploiting the properties of such an operator, it is possible to show that the alternating direction method of multipliers (ADMM) can detect infeasible problems. Although ADMM iterates diverge when the problem at hand is unsolvable, the differences between subsequent iterates converge to a constant vector which is also a certificate of primal and/or dual infeasibility. Reliable termination criteria for detecting infeasibility are proposed based on this result. Similar ideas are used to derive necessary and sufficient conditions for linear (geometric) convergence of an operator splitting method and a bound on the achievable convergence rate. The new bound turns out to be tight for the class of averaged operators. Next, the OSQP solver is presented. OSQP is a novel general-purpose solver for quadratic programs (QPs) based on ADMM. The solver is very robust, is able to detect infeasible problems, and has been extensively tested on many problem instances from a wide variety of application areas. Finally, operator splitting methods can also be effective in nonconvex optimization. The developed algorithm significantly outperforms a common approach based on convex relaxation of the original nonconvex problem.

Subjects/Keywords: Mathematical optimization; Convex optimization; Operator splitting methods; Infeasibility detection; Linear convergence

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APA (6^th Edition):

Banjac, G. (2018). Operator splitting methods for convex optimization : analysis and implementation. (Doctoral Dissertation). University of Oxford. Retrieved from https://ora.ox.ac.uk/objects/uuid:17ac73af-9fdf-4cf6-a946-3048da3fc9c2 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740972

Chicago Manual of Style (16^th Edition):

Banjac, Goran. “Operator splitting methods for convex optimization : analysis and implementation.” 2018. Doctoral Dissertation, University of Oxford. Accessed October 15, 2019. https://ora.ox.ac.uk/objects/uuid:17ac73af-9fdf-4cf6-a946-3048da3fc9c2 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740972.

MLA Handbook (7^th Edition):

Banjac, Goran. “Operator splitting methods for convex optimization : analysis and implementation.” 2018. Web. 15 Oct 2019.

Vancouver:

Banjac G. Operator splitting methods for convex optimization : analysis and implementation. [Internet] [Doctoral dissertation]. University of Oxford; 2018. [cited 2019 Oct 15]. Available from: https://ora.ox.ac.uk/objects/uuid:17ac73af-9fdf-4cf6-a946-3048da3fc9c2 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740972.

Council of Science Editors:

Banjac G. Operator splitting methods for convex optimization : analysis and implementation. [Doctoral Dissertation]. University of Oxford; 2018. Available from: https://ora.ox.ac.uk/objects/uuid:17ac73af-9fdf-4cf6-a946-3048da3fc9c2 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.740972

Lehigh University

27. Kuang, Xiaolong. Conic Programming Approaches for Polynomial Optimization: Theory and Applications.

Degree: PhD, Industrial Engineering, 2017, Lehigh University

URL: https://preserve.lehigh.edu/etd/2952

► Historically, polynomials are among the most popular class of functions used for empirical modeling in science and engineering. Polynomials are easy to evaluate, appear naturally… (more)

▼ Historically, polynomials are among the most popular class of functions used for empirical modeling in science and engineering. Polynomials are easy to evaluate, appear naturally in many physical (real-world) systems, and can be used to accurately approximate any smooth function. It is not surprising then, that the task of solving polynomial optimization problems; that is, problems where both the objective function and constraints are multivariate polynomials, is ubiquitous and of enormous interest in these fields. Clearly, polynomial op- timization problems encompass a very general class of non-convex optimization problems, including key combinatorial optimization problems.The focus of the first three chapters of this document is to address the solution of polynomial optimization problems in theory and in practice, using a conic optimization approach. Convex optimization has been well studied to solve quadratic constrained quadratic problems. In the first part, convex relaxations for general polynomial optimization problems are discussed. Instead of using the matrix space to study quadratic programs, we study the convex relaxations for POPs through a lifted tensor space, more specifically, using the completely positive tensor cone and the completely positive semidefinite tensor cone. We show that tensor relaxations theoretically yield no-worse global bounds for a class of polynomial optimization problems than relaxation for a QCQP reformulation of the POPs. We also propose an approximation strategy for tensor cones and show empirically the advantage of the tensor relaxation.In the second part, we propose an alternative SDP and SOCP hierarchy to obtain global bounds for general polynomial optimization problems. Comparing with other existing SDP and SOCP hierarchies that uses higher degree sum of square (SOS) polynomials and scaled diagonally sum of square polynomials (SDSOS) when the hierarchy level increases, these proposed hierarchies, using fixed degree SOS and SDSOS polynomials but more of these polynomials, perform numerically better. Numerical results show that the hierarchies we proposed have better performance in terms of tightness of the bound and solution time compared with other hierarchies in the literature.The third chapter deals with Alternating Current Optimal Power Flow problem via a polynomial optimization approach. The Alternating Current Optimal Power Flow (ACOPF) problem is a challenging non-convex optimization problem in power systems. Prior research mainly focuses on using SDP relaxations and SDP-based hierarchies to address the solution of ACOPF problem. In this Chapter, we apply existing SOCP hierarchies to this problem and explore the structure of the network to propose simplified hierarchies for ACOPF problems. Compared with SDP approaches, SOCP approaches are easier to solve and can be used to approximate large scale ACOPF problems.The last chapter also relates to the use of conic optimization techniques, but in this case to pricing in markets with non-convexities. Indeed, it is an… Advisors/Committee Members: Zuluaga, Luis F..

Subjects/Keywords: Conic Programming; Convex Optimization; Polynomial Optimization; Industrial Engineering

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APA (6^th Edition):

Kuang, X. (2017). Conic Programming Approaches for Polynomial Optimization: Theory and Applications. (Doctoral Dissertation). Lehigh University. Retrieved from https://preserve.lehigh.edu/etd/2952

Chicago Manual of Style (16^th Edition):

Kuang, Xiaolong. “Conic Programming Approaches for Polynomial Optimization: Theory and Applications.” 2017. Doctoral Dissertation, Lehigh University. Accessed October 15, 2019. https://preserve.lehigh.edu/etd/2952.

MLA Handbook (7^th Edition):

Kuang, Xiaolong. “Conic Programming Approaches for Polynomial Optimization: Theory and Applications.” 2017. Web. 15 Oct 2019.

Vancouver:

Kuang X. Conic Programming Approaches for Polynomial Optimization: Theory and Applications. [Internet] [Doctoral dissertation]. Lehigh University; 2017. [cited 2019 Oct 15]. Available from: https://preserve.lehigh.edu/etd/2952.

Council of Science Editors:

Kuang X. Conic Programming Approaches for Polynomial Optimization: Theory and Applications. [Doctoral Dissertation]. Lehigh University; 2017. Available from: https://preserve.lehigh.edu/etd/2952

Northeastern University

28. Moharrer, Armin. Distributing Frank-Wolfe via map-reduce.

Degree: MS, Department of Electrical and Computer Engineering, 2018, Northeastern University

URL: http://hdl.handle.net/2047/D20290439

► Large-scale optimization problems abound in data mining and machine learning applications, and the computational challenges they pose are often addressed through parallelization. We identify structural… (more)

Subjects/Keywords: convex optimization; distributed algorithms; distributed optimization; Frank-Wolfe; map-reduce; spark

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APA (6^th Edition):

Moharrer, A. (2018). Distributing Frank-Wolfe via map-reduce. (Masters Thesis). Northeastern University. Retrieved from http://hdl.handle.net/2047/D20290439

Chicago Manual of Style (16^th Edition):

Moharrer, Armin. “Distributing Frank-Wolfe via map-reduce.” 2018. Masters Thesis, Northeastern University. Accessed October 15, 2019. http://hdl.handle.net/2047/D20290439.

MLA Handbook (7^th Edition):

Moharrer, Armin. “Distributing Frank-Wolfe via map-reduce.” 2018. Web. 15 Oct 2019.

Vancouver:

Moharrer A. Distributing Frank-Wolfe via map-reduce. [Internet] [Masters thesis]. Northeastern University; 2018. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/2047/D20290439.

Council of Science Editors:

Moharrer A. Distributing Frank-Wolfe via map-reduce. [Masters Thesis]. Northeastern University; 2018. Available from: http://hdl.handle.net/2047/D20290439

Texas A&M University

29. Wang, Xu. Contributions to Resource Allocation in Cognitive Radio Networks.

Degree: PhD, Electrical Engineering, 2017, Texas A&M University

URL: http://hdl.handle.net/1969.1/165774

► The continuous increase in the number of wireless devices and the huge demand for higher data rates have promoted the development of new wireless communications… (more)

▼ The continuous increase in the number of wireless devices and the huge demand for higher data rates have promoted the development of new wireless communications technologies with improved spectrum sharing features. Recently, the concept of cognitive radio (CR) has gained increased popularity for the efficient utilization of radio frequency (RF) spectrum. A CR is characterized as a communication system which is capable to learn the spectrum environment through sensing, and to adapt its signaling schemes for a better utilization of the radio frequency resources. Resource allocation, which involves scheduling of spectrum and power resources, represents a crucial problem for the performance of CR networks in terms of system throughput and bandwidth utilization. In this dissertation, we investigate resource allocation problems in a CR network by exploring a variety of optimization techniques. Specifically, in the first part of the dissertation, our goal is to maximize the total throughput of secondary users (SUs) in an orthogonal frequency division multiple access (OFDMA) CR network. In addition, the power of SUs is controlled to keep the interference introduced to primary users (PUs) under certain limits, which gives rise to a non-convex mixed integer non-linear programming (MINLP) optimization problem. It is illustrated that the original non-convex MINLP formulation admits a special structure and the optimal solution can be achieved efficiently using any standard convex optimization method under a general and practical assumption. In the second part of the dissertation, considering the imperfect sensing information, we study the joint spectrum sensing and resource allocation problem in a multi-channel-multi-user CR network. The average total throughput of SUs is maximized by jointly optimizing the sensing threshold and power allocation strategies. The problem is also formulated as a non-convex MINLP problem. By utilizing the continuous relaxation and convex optimization tools, the dimension of the non-convex MINLP problem is significantly reduced, which helps to reformulate the optimization problem without resorting to integer variables. A newly-developed optimization technique, referred to as the monotonic optimization, is then employed to obtain an optimal solution. Furthermore, a practical low-complexity spectrum sensing and resource allocation algorithm is proposed to reduce the computational cost. Advisors/Committee Members: Serpedin, Erchin (advisor), Qaraqe, Khalid A (advisor), Zhang, Xi (committee member), Stoleru, Radu (committee member).

Subjects/Keywords: Cognitive radio; resource allocation; spectrum sensing; convex optimization; monotonic optimization

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APA (6^th Edition):

Wang, X. (2017). Contributions to Resource Allocation in Cognitive Radio Networks. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/165774

Chicago Manual of Style (16^th Edition):

Wang, Xu. “Contributions to Resource Allocation in Cognitive Radio Networks.” 2017. Doctoral Dissertation, Texas A&M University. Accessed October 15, 2019. http://hdl.handle.net/1969.1/165774.

MLA Handbook (7^th Edition):

Wang, Xu. “Contributions to Resource Allocation in Cognitive Radio Networks.” 2017. Web. 15 Oct 2019.

Vancouver:

Wang X. Contributions to Resource Allocation in Cognitive Radio Networks. [Internet] [Doctoral dissertation]. Texas A&M University; 2017. [cited 2019 Oct 15]. Available from: http://hdl.handle.net/1969.1/165774.

Council of Science Editors:

Wang X. Contributions to Resource Allocation in Cognitive Radio Networks. [Doctoral Dissertation]. Texas A&M University; 2017. Available from: http://hdl.handle.net/1969.1/165774

University of California – Berkeley

30. Godwin, Mark Franklin. Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization.

Degree: Mechanical Engineering, 2011, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/7fw187gd

► The growing prevalence of networked systems with local sensing and computational capability will result in an increasing array of online and large scale optimization problems.… (more)

▼ The growing prevalence of networked systems with local sensing and computational capability will result in an increasing array of online and large scale optimization problems. We adopt the framework of online convex optimization that allows for the optimization of an arbitrary sequence of convex functions subject to a single convex constraint set. We identify quasi-Newton algorithms as a promising class of algorithms to solve online strongly convex optimization problems. We first examine the relationships between several known algorithms for convex functions that satisfy a α-exp-concave assumption. Next we present two new quasi-Newton algorithms for non-smooth strongly convex functions and show how these algorithms can be parallelized given a summed objective function. Our new algorithms require fewer parameters and have provably tighter bounds then similar known algorithms. Also, our bounds are not a function of the number of iterations, but instead a function of the sequence of strongly convex parameters that correspond to a sequence of strongly convex functions. We then extend these algorithms to use a block diagonal hessian approximation. An algorithm with a fully diagonal hessian approximation results in a large scale quasi-Newton algorithm for online convex optimization. Our results can be translated to convergence bounds and optimization algorithms that solve non-smooth strongly convex functions. We perform numerical experiments on test functions of different dimension and compare our algorithms to similar known algorithms. These experiments show our algorithms perform well in the majority of test cases we consider. We apply our algorithms to online portfolio optimization with a l₂-norm regularized constant-rebalanced portfolio model and compare our algorithm to known methods. In addition, a heuristic algorithm for online vehicle routing is presented. Although online vehicle routing does not fit within the framework of online convex optimization, the work provided significant insight into online optimization and provides a future source of ideas and motivation. Finally, we provide conclusions and discuss future research directions.

Subjects/Keywords: Electrical engineering; Mechanical engineering; Computer science; online convex optimization; quasi-Newton; strongly convex

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APA (6^th Edition):

Godwin, M. F. (2011). Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/7fw187gd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Godwin, Mark Franklin. “Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization.” 2011. Thesis, University of California – Berkeley. Accessed October 15, 2019. http://www.escholarship.org/uc/item/7fw187gd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Godwin, Mark Franklin. “Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization.” 2011. Web. 15 Oct 2019.

Vancouver:

Godwin MF. Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization. [Internet] [Thesis]. University of California – Berkeley; 2011. [cited 2019 Oct 15]. Available from: http://www.escholarship.org/uc/item/7fw187gd.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Godwin MF. Quasi-Newton Algorithms for Non-smooth Online Strongly Convex Optimization. [Thesis]. University of California – Berkeley; 2011. Available from: http://www.escholarship.org/uc/item/7fw187gd

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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