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1 
Duality and normnumerical rangesSaunders, Benjamin David, January 1975 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1975. / Vita. Typescript. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (leaves 4244.).

2 
Surrogate constraint duality and extensions in integer programmingKarwan, Mark H. 12 1900 (has links)
No description available.

3 
A duality theory for Banach spaces with the Convex PointofContinuity PropertyHare, David Edwin George January 1987 (has links)
A norm ⋅ on a Banach space X is Fréchet differentiable at x ∈ X if there is a functional ∫∈ X* such that [Formula Omitted] This concept reflects the smoothness characteristics of X. A dual Banach space X* has the RadonNikodym Property (RNP) if whenever C ⊂ X* is weak*compact and convex, and ∈ > 0, there is an x ∈ X and an ⍺ > 0 such that diameter [Formula Omitted] this property reflects the convexity characteristics of X*.
Culminating several years of work by many researchers, the following theorem established a strong connection between the smoothness of X and the convexity of X*: Every equivalent norm on X is Fréchet differentiable on a dense set if and only if X* has the RNP.
A more general measure of convexity has been recently receiving a great deal of attention: A dual Banach space X* has the weak* Convex PointofContinuity Property (C*PCP) if whenever ɸ ≠ C ⊂ X* is weak*compact and convex, and ∈ > 0, there is a weak*open set V such that V ⋂ C ≠ ɸ and diam V ⋂ C < ∈.
In this thesis, we develop the corresponding smoothness properties of X which are dual to C*PCP. For this, a new type of differentiability, called cofinite Fréchet differentiability, is introduced, and we establish the following theorem: Every equivalent norm on X is cofinitely Fréchet differentiable everywhere if and only if X* has the C*PCP.
Representing joint work with R. Deville, G. Godefroy and V. Zizler, an alternate
approach is developed in the case when X is separable. We show that if X is separable, then every equivalent norm on X which has a strictly convex dual is Fréchet differentiable on a dense set if and only if X* has the C*PCP, if and only if every equivalent norm on X which is Gâteaux differentiable (everywhere) is Fréchet differentiable on a dense set. This result is used to show that if X* does not have the C*PCP, then there is a subspace Y of X such that neither Y* nor (X/Y)* have the C*PCP, yet both Y and X/Y have finite dimensional Schauder decompositions. The corresponding result for spaces X* failing the RNP remains open. / Science, Faculty of / Mathematics, Department of / Graduate

4 
Quadratic 01 programming: geometric methods and duality analysis. / CUHK electronic theses & dissertations collectionJanuary 2008 (has links)
In part I of this dissertation, certain rich geometric properties hidden behind quadratic 01 programming are investigated. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 01 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 01 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branchandbound 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 NPhardness 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 stateoftheart 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: 7006, Section: B, page: 3764. / Thesis (Ph.D.)Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 140153). / 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.

5 
Theory and algorithms for separated continuous linear programming and its extensions. / CUHK electronic theses & dissertations collectionJanuary 2005 (has links)
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 polynomialtime approximation (PTA) scheme. The tradeoff 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 DaWei Yao. / Source: Dissertation Abstracts International, Volume: 6701, Section: B, page: 0520. / Thesis (Ph.D.)Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 122127). / 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.

6 
Optimal control of hereditary differential system.January 1985 (has links)
by Yung SiuPang. / Includes bibliographical references / Thesis (M.Ph.)Chinese University of Hong Kong, 1985

7 
Duality theory, saddle point problem and vector optimization in distributed systems.January 1985 (has links)
by Lau Waitong. / Bibliography: leaves 4547 / Thesis (M.Ph.)Chinese University of Hong Kong, 1985

8 
Duality theory by sum of epigraphs of conjugate functions in semiinfinite convex optimization.January 2009 (has links)
Lau, Fu Man. / Thesis (M.Phil.)Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 9497). / 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  Setvalued 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  Interiorpoint 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 semiinfinite optimization via weakly* sum of epigraph of conjugate functions  p.70 / Chapter 4.1  Introduction  p.70 / Chapter 4.2  Fenchel duality in semiinfinite convex optimization  p.73 / Chapter 4.3  Sufficient conditions for Fenchel duality in semiinfinite convex optimization  p.79 / Chapter 4.3.1  Continuous realvalued functions  p.80 / Chapter 4.3.2  Nonnegativevalued functions  p.84 / Bibliography  p.94

9 
Duality of higher order nonEuclidean property for oriented matroidsJunes, Leandro. January 2008 (has links)
Thesis (Ph. D.)State University of New York at Binghamton, Department of Mathematical Sciences, 2008. / Includes bibliographical references.

10 
Zelluläre Modelkategorien und GrothendieckVerdier Dualität in der verallgemeinerten KohomologieAdleff, Jürgen. January 1900 (has links)
Thesis (doctoral)Rheinische FriedrichWilhelmsUniversität Bonn, 2000. / Includes bibliographical references (p. 8385).

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