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You searched for +publisher:"Clemson University" +contributor:("Dr. Cole Smith"). Showing records 1 – 2 of 2 total matches.

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Clemson University

1. Xu, Yibo. Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions.

Degree: PhD, Mathematical Sciences, 2018, Clemson University

Motivated by a variety of problems in global optimization and integer programming that involve multilinear expressions of discrete or continuous variables, this research derives approxima-tions of multilinear functions, and studies the accuracy of these approximations through worst-case error-analyses: • The derivation of the convex hull representations of large families of symmetric multilinear polynomials (SMPs) that are defined over box constraints through geometrical exploitation of the polytope symmetry and specially designed facet generation method; and • The identification of the set of all points at which a nonnegative multilinear polynomial on a box vanishes, which applies to the identification of the set of all points which satisfy any facet at equality. • The worst-case error analysis associated with linearizations of monomial expressions in boun-ded discrete and/or continuous variables: for certain families of variable-bound structures, the worst-case errors associated with convex hull forms are studied, along with the identification of all points which produce these errors. • The worst-case error analysis associated with replacing the multilinear monomial term with a “best” approximating linear function, in contrast to the previous item on “convex hull linearization:” using the results of the first item, explicit convex hull forms are exploited to identify the “best” linear functions. Advisors/Committee Members: Dr. Warren Adams, Committee Chair, Dr. Xuhong Gao, Dr. Matthew Saltzman, Dr. Cole Smith.

Subjects/Keywords: convex hull; error analysis; facet; multilinear polynomial; symmetry

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

APA (6th Edition):

Xu, Y. (2018). Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/2094

Chicago Manual of Style (16th Edition):

Xu, Yibo. “Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions.” 2018. Doctoral Dissertation, Clemson University. Accessed October 15, 2019. https://tigerprints.clemson.edu/all_dissertations/2094.

MLA Handbook (7th Edition):

Xu, Yibo. “Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions.” 2018. Web. 15 Oct 2019.

Vancouver:

Xu Y. Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions. [Internet] [Doctoral dissertation]. Clemson University; 2018. [cited 2019 Oct 15]. Available from: https://tigerprints.clemson.edu/all_dissertations/2094.

Council of Science Editors:

Xu Y. Convex Hulls, Relaxations, and Approximations of General Monomials and Multilinear Functions. [Doctoral Dissertation]. Clemson University; 2018. Available from: https://tigerprints.clemson.edu/all_dissertations/2094


Clemson University

2. Dranichak, Garrett M. Robust Solutions to Uncertain Multiobjective Programs.

Degree: PhD, Mathematical Sciences, 2018, Clemson University

Decision making in the presence of uncertainty and multiple conflicting objec-tives is a real-life issue, especially in the fields of engineering, public policy making, business management, and many others. The conflicting goals may originate from the variety of ways to assess a system’s performance such as cost, safety, and affordability, while uncertainty may result from inaccurate or unknown data, limited knowledge, or future changes in the environment. To address optimization problems that incor-porate these two aspects, we focus on the integration of robust and multiobjective optimization. Although the uncertainty may present itself in many different ways due to a diversity of sources, we address the situation of objective-wise uncertainty only in the coefficients of the objective functions, which is drawn from a finite set of scenarios. Among the numerous concepts of robust solutions that have been proposed and de-veloped, we concentrate on a strict concept referred to as highly robust efficiency in which a feasible solution is highly robust efficient provided that it is efficient with respect to every realization of the uncertain data. The main focus of our study is uncertain multiobjective linear programs (UMOLPs), however, nonlinear problems are discussed as well. In the course of our study, we develop properties of the highly robust efficient set, provide its characterization using the cone of improving directions associated with the UMOLP, derive several bound sets on the highly robust efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the polar and strict polar of the cone of improving directions, as well as the acuteness of this cone, we derive properties and closed-form representations of the (strict) polar and also propose methods to verify the property of acuteness. Moreover, we undertake the computation of highly robust efficient solutions. We provide methods for checking whether or not the highly robust efficient set is empty, computing highly robust efficient points, and determining whether a given solution of interest is highly robust efficient. An application in the area of bank management is included. Advisors/Committee Members: Dr. Margaret Wiecek, Committee Chair, Dr. Warren Adams, Dr. Herve Kerivin, Dr. Matthew Saltzman, Dr. Cole Smith.

Subjects/Keywords: highly robust efficient; objective-wise uncertainty; robust multiobjective optimization; uncertain multiobjective programs

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

APA (6th Edition):

Dranichak, G. M. (2018). Robust Solutions to Uncertain Multiobjective Programs. (Doctoral Dissertation). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_dissertations/2154

Chicago Manual of Style (16th Edition):

Dranichak, Garrett M. “Robust Solutions to Uncertain Multiobjective Programs.” 2018. Doctoral Dissertation, Clemson University. Accessed October 15, 2019. https://tigerprints.clemson.edu/all_dissertations/2154.

MLA Handbook (7th Edition):

Dranichak, Garrett M. “Robust Solutions to Uncertain Multiobjective Programs.” 2018. Web. 15 Oct 2019.

Vancouver:

Dranichak GM. Robust Solutions to Uncertain Multiobjective Programs. [Internet] [Doctoral dissertation]. Clemson University; 2018. [cited 2019 Oct 15]. Available from: https://tigerprints.clemson.edu/all_dissertations/2154.

Council of Science Editors:

Dranichak GM. Robust Solutions to Uncertain Multiobjective Programs. [Doctoral Dissertation]. Clemson University; 2018. Available from: https://tigerprints.clemson.edu/all_dissertations/2154

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