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You searched for subject:(Rank Constrained Optimization). Showing records 1 – 3 of 3 total matches.

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Lehigh University

1. Arastoo, Reza. Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies.

Degree: PhD, Mechanical Engineering, 2016, Lehigh University

This dissertation is about control, identification, and analysis of systems with sparse interconnection topologies. We address two main research objectives relating to sparsity in control systems and networks. The first problem is optimal sparse controller synthesis, and the second one is the identification of sparse network. The first part of this dissertation starts with the chapter focusing on developing theoretical frameworks for the synthesis of optimal sparse output feedback controllers under pre-specified structural constraints. This is achieved by establishing a balance between the stability of the controller and the systems quadratic performance. Our approach is mainly based on converting the problem into rank constrained optimizations.We then propose a new approach in the syntheses of sparse controllers by em- ploying the concept of Hp approximations. Considering the trade-off between the controller sparsity and the performance deterioration due to the sparsification pro- cess, we propose solving methodologies in order to obtain robust sparse controllers when the system is subject to parametric uncertainties.Next, we pivot our attention to a less-studied notion of sparsity, namely row sparsity, in our optimal controller design. Combining the concepts from the majorization theory and our proposed rank constrained formulation, we propose an exact reformulation of the optimal state feedback controllers with strict row sparsity constraint, which can be sub-optimally solved by our proposed iterative optimization techniques. The second part of this dissertation focuses on developing a theoretical framework and algorithms to derive linear ordinary differential equation models of gene regulatory networks using literature curated data and micro-array data. We propose several algorithms to derive stable sparse network matrices. A thorough comparison of our algorithms with the existing methods are also presented by applying them to both synthetic and experimental data-sets. Advisors/Committee Members: Kothare, Mayuresh V..

Subjects/Keywords: Alternating Direction Method of Multipliers; Convex Optimization; Rank Constrained Optimization; Row Sparsity; Sparse Controller Synthesis; Engineering; Mechanical Engineering

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APA (6th Edition):

Arastoo, R. (2016). Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies. (Doctoral Dissertation). Lehigh University. Retrieved from https://preserve.lehigh.edu/etd/2493

Chicago Manual of Style (16th Edition):

Arastoo, Reza. “Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies.” 2016. Doctoral Dissertation, Lehigh University. Accessed July 02, 2020. https://preserve.lehigh.edu/etd/2493.

MLA Handbook (7th Edition):

Arastoo, Reza. “Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies.” 2016. Web. 02 Jul 2020.

Vancouver:

Arastoo R. Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies. [Internet] [Doctoral dissertation]. Lehigh University; 2016. [cited 2020 Jul 02]. Available from: https://preserve.lehigh.edu/etd/2493.

Council of Science Editors:

Arastoo R. Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies. [Doctoral Dissertation]. Lehigh University; 2016. Available from: https://preserve.lehigh.edu/etd/2493

2. Sun, Chuangchuang. Rank-Constrained Optimization: Algorithms and Applications.

Degree: PhD, Aero/Astro Engineering, 2018, The Ohio State University

Matrix rank related optimization problems comprise rank-constrained optimizationproblems (RCOPs) and rank minimization problems, which involve the matrix rank functionin the objective or the constraints. General RCOPs are defined to optimize a convex objectivefunction subject to a set of convex constraints and rank constraints on unknown rectangularmatrices. RCOPs have received extensive attention due to their wide applications in signalprocessing, model reduction, and system identification, just to name a few. Noteworthily,The general/nonconvex quadratically constrained quadratic programming (QCQP) problemwith wide applications is a special category of RCOP. On the other hand, when the rankfunction appears in the objective of an optimization problem, it turns out to be a rankminimization problem (RMP), classified as another category of nonconvex optimization.Applications of RMPs have been found in a variety of areas, such as matrix completion,control system analysis and design, and machine learning.At first, RMP and RCOPs are not isolated. Though we can transform a RMP into aRCOP by introducing a slack variable, the reformulated RCOP, however, has an unknownupper bound for the rank function. That is a big shortcoming. Provided that a given matrixupper bounded is a prerequisite for most of the algorithms when solving RCOPs, we firstfill this gap by demonstrating that RMPs can be equivalently transformed into RCOPs byintroducing a quadratic matrix equality constraint. Furthermore, the wide application ofRMPs and RCOPs attract extensive studies aiming at developing efficient optimization algorithms to solve the challenging matrix-related optimization problems. Motivated by thelimitations of existing algorithms, we aim to develop effective and efficient algorithms tosolve rank-related optimization problems. Two classes of algorithms and their variants areproposed here.The first algorithm, based on the alternating minimization, is named iterative rank minimization (IRM). The IRM method, with each sequential problem formulated as a convexoptimization problem, aims to solve general RCOPs, where the constrained rank could beany assigned integer number. Although IRM is primarily designed for RCOPs with rankconstraints on positive semidefinite matrices, a semidefinite embedding lemma is introducedto extend IRM to RCOPs with rank constraints on general rectangular matrices. Moreover,The proposed IRM method is applicable to RCOPs with rank inequalities constrained byupper or lower bounds, as well as rank equality constraints. Convergence of IRM is provedvia the duality theory and the Karush-KuhnTucker conditions. Furthermore, the conversionfrom RMPs to RCOPs and the proposed IRM method are applied to solve cardinality minimization problems and cardinality-constrained optimization problems, which are handled asspecial cases of RMPs and RCOPs, respectively. To verify the effectiveness and improvedperformance of the proposed IRM method, representative applications, including matrixcompletion, system identification, output feedback… Advisors/Committee Members: Dai, Ran (Advisor).

Subjects/Keywords: Aerospace Engineering; Computer Science; Computer Engineering; Engineering; Electrical Engineering; optimization, rank-constrained optimization

…1 1.1 1.2 1.3 General Rank-Constrained Optimization… …2.1.1 Rank-Constrained Optimization Problems . . . . . . . . . . . . 2.1.2 Rank Minimization… …to Rank Constrained Optimization Problems . . . 2.2.2 IRM Approach to RMPs… …29 29 30 34 35 35 37 41 41 47 60 74 84 ADMM for Rank Constrained Optimization… …QCQPs into Rank-One Constrained Optimization Problems… 

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

APA (6th Edition):

Sun, C. (2018). Rank-Constrained Optimization: Algorithms and Applications. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1531750343188114

Chicago Manual of Style (16th Edition):

Sun, Chuangchuang. “Rank-Constrained Optimization: Algorithms and Applications.” 2018. Doctoral Dissertation, The Ohio State University. Accessed July 02, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531750343188114.

MLA Handbook (7th Edition):

Sun, Chuangchuang. “Rank-Constrained Optimization: Algorithms and Applications.” 2018. Web. 02 Jul 2020.

Vancouver:

Sun C. Rank-Constrained Optimization: Algorithms and Applications. [Internet] [Doctoral dissertation]. The Ohio State University; 2018. [cited 2020 Jul 02]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1531750343188114.

Council of Science Editors:

Sun C. Rank-Constrained Optimization: Algorithms and Applications. [Doctoral Dissertation]. The Ohio State University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1531750343188114

3. ZHOU PAN. STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES.

Degree: 2019, National University of Singapore

Subjects/Keywords: structured data analysis; low-rank tensor analysis; constrained optimization; Riemannian optimization; deep learning theory; generalization theory

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

APA (6th Edition):

PAN, Z. (2019). STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES. (Thesis). National University of Singapore. Retrieved from https://scholarbank.nus.edu.sg/handle/10635/167559

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

Chicago Manual of Style (16th Edition):

PAN, ZHOU. “STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES.” 2019. Thesis, National University of Singapore. Accessed July 02, 2020. https://scholarbank.nus.edu.sg/handle/10635/167559.

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

MLA Handbook (7th Edition):

PAN, ZHOU. “STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES.” 2019. Web. 02 Jul 2020.

Vancouver:

PAN Z. STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES. [Internet] [Thesis]. National University of Singapore; 2019. [cited 2020 Jul 02]. Available from: https://scholarbank.nus.edu.sg/handle/10635/167559.

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

Council of Science Editors:

PAN Z. STRUCTURED DATA ANALYSIS: MODELS, ALGORITHMS AND THEORIES. [Thesis]. National University of Singapore; 2019. Available from: https://scholarbank.nus.edu.sg/handle/10635/167559

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

.