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Recent developments in optimality notions, scalarizations and optimality conditions in vector optimization. / Recent developments in vector optimization

Lee, Hon Leung. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 98-101) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Preliminaries --- p.11 / Chapter 2.1 --- Functional analysis --- p.11 / Chapter 2.2 --- Convex analysis --- p.14 / Chapter 2.3 --- Relative interiors --- p.19 / Chapter 2.4 --- Multifunctions --- p.21 / Chapter 2.5 --- Variational analysis --- p.22 / Chapter 3 --- A unified notion of optimality --- p.29 / Chapter 3.1 --- Basic notions of minimality --- p.29 / Chapter 3.2 --- A unified notion --- p.32 / Chapter 4 --- Separation theorems --- p.38 / Chapter 4.1 --- Zheng and Ng fuzzy separation theorem --- p.38 / Chapter 4.2 --- Extremal principles and other consequences --- p.43 / Chapter 5 --- Necessary conditions for the unified notion of optimality --- p.49 / Chapter 5.1 --- Local asymptotic closedness --- p.49 / Chapter 5.2 --- First order necessary conditions --- p.56 / Chapter 5.2.1 --- Introductory remark --- p.56 / Chapter 5.2.2 --- Without operator constraints --- p.59 / Chapter 5.2.3 --- With operator constraints --- p.66 / Chapter 5.3 --- Comparisons with known necessary conditions --- p.74 / Chapter 5.3.1 --- Finite-dimensional setting --- p.74 / Chapter 5.3.2 --- Zheng and Ng's work --- p.76 / Chapter 5.3.3 --- Dutta and Tammer's work --- p.80 / Chapter 5.3.4 --- Bao and Mordukhovich's previous work --- p.81 / Chapter 6 --- A weak notion: approximate efficiency --- p.84 / Chapter 6.1 --- Approximate minimality --- p.85 / Chapter 6.2 --- A scalarization result --- p.86 / Chapter 6.3 --- Variational approach --- p.94 / Bibliography --- p.98 / Index --- p.102

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327577
Date January 2011
ContributorsLee, Hon Leung., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 104 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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