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Distance-two constrained labellings of graphs and related problemsGu, Guohua 01 January 2005 (has links)
No description available.
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Duality theory by sum of epigraphs of conjugate functions in semi-infinite convex optimization.January 2009 (has links)
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
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Convex optimization under inexact first-order informationLan, Guanghui. January 2009 (has links)
Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Convexity, convergence and feedback in optimal control /Goebel, Rafal, January 2000 (has links)
Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 120-124).
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Lagrangian duality in convex optimization.January 2009 (has links)
Li, Xing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 76-80). / Abstract also in Chinese. / Introduction --- p.4 / Chapter 1 --- Preliminary --- p.6 / Chapter 1.1 --- Notations --- p.6 / Chapter 1.2 --- On Properties of Epigraphs --- p.10 / Chapter 1.3 --- Subdifferential Calculus --- p.14 / Chapter 1.4 --- Conical Approximations --- p.16 / Chapter 2 --- Duality in the Cone-convex System --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- Various of Constraint Qualifications --- p.28 / Chapter 2.2.1 --- Slater´ةs Condition Revisited --- p.28 / Chapter 2.2.2 --- The Closed Cone Constrained Qualification --- p.31 / Chapter 2.2.3 --- The Basic Constraint Qualification --- p.38 / Chapter 2.3 --- Lagrange Multiplier and the Geometric Multiplier --- p.45 / Chapter 3 --- Stable Lagrangian Duality --- p.48 / Chapter 3.1 --- Introduction --- p.48 / Chapter 3.2 --- Stable Farkas Lemma --- p.48 / Chapter 3.3 --- Stable Duality --- p.57 / Chapter 4 --- Sequential Lagrange Multiplier Conditions --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- The Sequential Lagrange Multiplier --- p.64 / Chapter 4.3 --- Application in Semi-Infinite Programs --- p.71 / Bibliography --- p.76 / List of Symbols --- p.80
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Differentiability of convex functions and Radon-Nikodym properties in Banach spaces /Ho, Kwok-hon. January 1983 (has links)
Thesis--M. Phil., University of Hong Kong, 1983.
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Differentiability of convex functions and Radon-Nikodym properties in Banach spaces何國漢, Ho, Kwok-hon. January 1983 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy
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Convex functionsZagar, Susanna Maria 01 January 1996 (has links)
No description available.
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Borel Sets with Convex Sections and Extreme Point SelectorsSchlee, Glen A. (Glen Alan) 08 1900 (has links)
In this dissertation separation and selection theorems are presented. It begins by presenting a detailed proof of the Inductive Definability Theorem of D. Cenzer and R.D. Mauldin, including their boundedness principle for monotone coanalytic operators.
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Plane Curves, Convex Curves, and Their Deformation Via the Heat EquationDebrecht, Johanna M. 08 1900 (has links)
We study the effects of a deformation via the heat equation on closed, plane curves. We begin with an overview of the theory of curves in R3. In particular, we develop the Frenet-Serret equations for any curve parametrized by arc length. This chapter is followed by an examination of curves in R2, and the resultant adjustment of the Frenet-Serret equations. We then prove the rotation index for closed, plane curves is an integer and for simple, closed, plane curves is ±1. We show that a curve is convex if and only if the curvature does not change sign, and we prove the Isoperimetric Inequality, which gives a bound on the area of a closed curve with fixed length. Finally, we study the deformation of plane curves developed by M. Gage and R. S. Hamilton. We observe that convex curves under deformation remain convex, and simple curves remain simple.
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