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
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326884 |
| Date | January 2009 |
| Contributors | Lau, Fu Man., 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, v, 97 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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