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Duality theory by sum of epigraphs of conjugate functions in semi-infinite convex optimization.

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

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326884
Date January 2009
ContributorsLau, Fu Man., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, v, 97 leaves ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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