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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_327577 |
| Date | January 2011 |
| Contributors | Lee, Hon Leung., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 104 leaves ; 30 cm. |
| Rights | Use 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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