Thesis (Ph. D.)--University of Wisconsin--Madison, 1975. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 42-44.).

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by Yung Siu-Pang. / Includes bibliographical references / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

by Lau Wai-tong. / Bibliography: leaves 45-47 / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

In part I of this dissertation, certain rich geometric properties hidden behind quadratic 0-1 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0-1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0-1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results. / In part II of this dissertation, we present new results of the duality gap between the binary quadratic optimization problem and its Lagrangian dual. We first derive a necessary and sufficient condition for the zero duality gap and discuss its relationship with the polynomial solvability of the problem. We then characterize the zeroness of duality gap by the distance, delta, between the binary set and certain affine space C. Finally, we discuss a computational procedure of the distance delta. These results provide new insights into the duality gap and polynomial solvability of binary quadratic optimization problems. / The unconstraint quadratic binary problem (UBQP), as a classical combinatorial problem, finds wide applications in broad field and human activities including engineering, science, finance, etc. The NP-hardness of the combinatorial problems makes a great challenge to solve the ( UBQP). The main purpose of this research is to develop high performance solution method for solving (UBQP) via the geometric properties of the objective ellipse contour and the optimal solution. This research makes several contributions to advance the state-of-the-art of geometric approach of (UBQP). These contributions include both theoretical and numerical aspects as stated below. / Liu, Chunli. / Adviser: Duan Li. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3764. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 140-153). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

In this thesis we study the theory and algorithms for separated continuous linear programming (SCLP) and its extensions. / Throughout this thesis, some numerical examples are used to illustrate the algorithms that we propose. In particular, we solve a special LQ control problem with sign constraints on the state and the control variables as an instance of SCCP, yielding a new solution method for such kind of LQ control problems. / We first investigate the relationships among SCLP, the dual of SCLP and the corresponding discretized versions of them. By using the symmetric primal and dual structure and an even partition of the time interval [0, T], we show that the strong duality holds between SCLP and its dual problem under some mild assumption. This is actually an alternative proof for the strong duality theorem. The other constructive proof is due to Weiss [50]. Our new proof is more direct and can be easily extended to prove the same strong duality results for the extensions of SCLP. Based on these results, we propose an approximation algorithm which solves SCLP with any prescribed precision requirement. Our algorithm is in fact a polynomial-time approximation (PTA) scheme. The trade-off between the quality of the solution and the computational effort is explicit. / We then study the extensions of SCLP; that is, separated continuous conic programming (SCCP) and its generalized version (GSCCP). It turns out that our results on SCLP can be readily extended to SCCP and GSCCP. To our knowledge, SCCP and GSCCP are new models with novel applications. / Wang Xiaoqing. / "June 2005." / Advisers: Shuzhong Zhang; David Da-Wei Yao. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0520. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 122-127). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Lau, Fu Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 94-97). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgements --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Notations and Preliminaries --- p.4 / Chapter 2.1 --- Introduction --- p.4 / Chapter 2.2 --- Basic notations --- p.4 / Chapter 2.3 --- On the properties of subdifferentials --- p.8 / Chapter 2.4 --- On the properties of normal cones --- p.9 / Chapter 2.5 --- Some computation rules for conjugate functions --- p.13 / Chapter 2.6 --- On the properties of epigraphs --- p.15 / Chapter 2.7 --- Set-valued analysis --- p.19 / Chapter 2.8 --- Weakly* sum of sets in dual spaces --- p.21 / Chapter 3 --- Sum of Epigraph Constraint Qualification (SECQ) --- p.31 / Chapter 3.1 --- Introduction --- p.31 / Chapter 3.2 --- Definition of the SECQ and its basic properties --- p.33 / Chapter 3.3 --- Relationship between the SECQ and other constraint qualifications --- p.39 / Chapter 3.3.1 --- The SECQ and the strong CHIP --- p.39 / Chapter 3.3.2 --- The SECQ and the linear regularity --- p.46 / Chapter 3.4 --- Interior-point conditions for the SECQ --- p.58 / Chapter 3.4.1 --- I is finite --- p.59 / Chapter 3.4.2 --- I is infinite --- p.61 / Chapter 4 --- Duality theory of semi-infinite optimization via weakly* sum of epigraph of conjugate functions --- p.70 / Chapter 4.1 --- Introduction --- p.70 / Chapter 4.2 --- Fenchel duality in semi-infinite convex optimization --- p.73 / Chapter 4.3 --- Sufficient conditions for Fenchel duality in semi-infinite convex optimization --- p.79 / Chapter 4.3.1 --- Continuous real-valued functions --- p.80 / Chapter 4.3.2 --- Nonnegative-valued functions --- p.84 / Bibliography --- p.94

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2008. / Includes bibliographical references.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 83-85).

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.