Pong Ting Kei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 79-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Notations --- p.7 / Chapter 2.3 --- On properties of Normal Cones --- p.9 / Chapter 2.4 --- Polar Calculus --- p.13 / Chapter 2.5 --- Notions of Relative Interior --- p.17 / Chapter 2.6 --- Properties of Minkowski functional --- p.18 / Chapter 2.7 --- Properties of Epigraphs --- p.19 / Chapter 3 --- The Strong Conical Hull Intersection Property (Strong CHIP): Definition and Some Properties --- p.22 / Chapter 3.1 --- Introduction --- p.22 / Chapter 3.2 --- Definition of the strong CHIP --- p.24 / Chapter 3.3 --- Relationship between the strong CHIP and projections onto sets --- p.26 / Chapter 3.4 --- Relationship between the strong CHIP and the Basic Constraint Qualifications (BCQ) --- p.35 / Chapter 3.5 --- The strong CHIP of extremal subsets --- p.42 / Chapter 4 --- Sufficient Conditions for the Strong CHIP --- p.46 / Chapter 4.1 --- Introduction --- p.46 / Chapter 4.2 --- ̐ưجI̐ưجis finite --- p.47 / Chapter 4.2.1 --- Interior point conditions --- p.47 / Chapter 4.2.2 --- Boundedly linear regularity --- p.52 / Chapter 4.2.3 --- Epi-sum --- p.54 / Chapter 4.3 --- ̐ưجI̐ưجis infinite --- p.56 / Chapter 4.3.1 --- A Sum Rule --- p.57 / Chapter 4.3.2 --- The C-Extended Minkowski Functional --- p.58 / Chapter 4.3.3 --- Relative Interior Point Conditions --- p.62 / Chapter 4.3.4 --- Bounded Linear Regularity --- p.68 / Chapter 5 --- "The SECQ, Linear Regularity and the Strong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces" --- p.69 / Chapter 5.1 --- Introduction --- p.69 / Chapter 5.2 --- The strong CHIP and the SECQ --- p.71 / Chapter 5.3 --- Linear regularity and the SECQ --- p.73 / Chapter 5.4 --- Interior-point conditions and the SECQ --- p.76 / Bibliography --- p.79

by Cheng Tak Wai, Johnny. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.7 / Chapter 2.1 --- Self-dual embedding --- p.7 / Chapter 2.2 --- Conic optimization --- p.8 / Chapter 2.3 --- Self-dual embedded conic optimization --- p.9 / Chapter 2.4 --- Connection with convex programming --- p.11 / Chapter 2.5 --- Chapter summary --- p.15 / Chapter 3 --- Implementation of the algorithm --- p.17 / Chapter 3.1 --- The new search direction --- p.17 / Chapter 3.2 --- Select the step-length --- p.23 / Chapter 3.3 --- The multi-constraint case --- p.25 / Chapter 3.4 --- Chapter summary --- p.32 / Chapter 4 --- Numerical results on randomly generated problem --- p.34 / Chapter 4.1 --- Single-constraint problems --- p.35 / Chapter 4.2 --- Multi-constraint problems --- p.36 / Chapter 4.3 --- Running time and the size of the problem --- p.39 / Chapter 4.4 --- Chapter summary --- p.42 / Chapter 5 --- Geometric optimization --- p.45 / Chapter 5.1 --- Geometric programming --- p.45 / Chapter 5.1.1 --- Monomials and posynomials --- p.45 / Chapter 5.1.2 --- Geometric programming --- p.46 / Chapter 5.1.3 --- Geometric program in convex form --- p.47 / Chapter 5.2 --- Conic transformation --- p.48 / Chapter 5.3 --- Computational results of geometric optimization problem --- p.50 / Chapter 5.4 --- Chapter summary --- p.55 / Chapter 6 --- Conclusion --- p.57

Lee, King Leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leave 95). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Organization --- p.10 / Chapter 2 --- Semigroups and Cones --- p.13 / Chapter 2.1 --- Relation between Semigroups and Cones --- p.13 / Chapter 2.2 --- Subadditive Functions on Semigroups --- p.23 / Chapter 2.3 --- Relation between Cones and Bases --- p.29 / Chapter 3 --- General Theories of Okounkov Bodies --- p.33 / Chapter 3.1 --- Okounkov Bodies and Volumes --- p.33 / Chapter 3.2 --- Relation of Subadditive Functions on Semigroups and Okounkov Bodies --- p.39 / Chapter 3.3 --- Convex Functions on Okounkov Bodies --- p.47 / Chapter 4 --- Okounkov Bodies and Complex Geometry --- p.55 / Chapter 4.1 --- Holomorphic Line Bundles --- p.55 / Chapter 4.2 --- Chebyshev Transform --- p.65 / Chapter 4.3 --- Bernstein-Markov Norms --- p.74 / Chapter 5 --- Applications of Okounkov Bodies --- p.81 / Chapter 5.1 --- Relative Energy of Weights --- p.81 / Chapter 5.2 --- Computational Methods and Some Examples --- p.89 / Bibliography --- p.95

No description available.

Thesis--Université de Paris XI. / Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 1987.

published_or_final_version / abstract / toc / Mathematics / Doctoral / Doctor of Philosophy

No description available.

No description available.

No description available.