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.iAcknowledgements --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Notations and Preliminaries --- p.4Chapter 2.1 --- Introduction --- p.4Chapter 2.2 --- Basic notations --- p.4Chapter 2.3 --- On the properties of subdifferentials --- p.8Chapter 2.4 --- On the properties of normal cones --- p.9Chapter 2.5 --- Some computation rules for conjugate functions --- p.13Chapter 2.6 --- On the properties of epigraphs --- p.15Chapter 2.7 --- Set-valued analysis --- p.19Chapter 2.8 --- Weakly* sum of sets in dual spaces --- p.21Chapter 3 --- Sum of Epigraph Constraint Qualification (SECQ) --- p.31Chapter 3.1 --- Introduction --- p.31Chapter 3.2 --- Definition of the SECQ and its basic properties --- p.33Chapter 3.3 --- Relationship between the SECQ and other constraint qualifications --- p.39Chapter 3.3.1 --- The SECQ and the strong CHIP --- p.39Chapter 3.3.2 --- The SECQ and the linear regularity --- p.46Chapter 3.4 --- Interior-point conditions for the SECQ --- p.58Chapter 3.4.1 --- I is finite --- p.59Chapter 3.4.2 --- I is infinite --- p.61Chapter 4 --- Duality theory of semi-infinite optimization via weakly* sum of epigraph of conjugate functions --- p.70Chapter 4.1 --- Introduction --- p.70Chapter 4.2 --- Fenchel duality in semi-infinite convex optimization --- p.73Chapter 4.3 --- Sufficient conditions for Fenchel duality in semi-infinite convex optimization --- p.79Chapter 4.3.1 --- Continuous real-valued functions --- p.80Chapter 4.3.2 --- Nonnegative-valued functions --- p.84Bibliography --- p.9