by Shiu-Tung Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 100-103). / Abstract also in Chinese. / Chapter 1 --- Preliminary --- p.5 / Chapter 1.1 --- Linear and Convex Optimization Model --- p.5 / Chapter 1.2 --- Notations for Linear Optimization --- p.5 / Chapter 1.3 --- Definition and Properties of Convexities --- p.7 / Chapter 1.4 --- Useful Theorem for Unconstrained Minimization --- p.10 / Chapter 2 --- Linear Optimization --- p.11 / Chapter 2.1 --- Self-dual Linear Optimization Model --- p.11 / Chapter 2.2 --- Definitions and Main Theorems --- p.14 / Chapter 2.3 --- Self-dual Embedding and Simple Example --- p.22 / Chapter 2.4 --- Newton step --- p.25 / Chapter 2.5 --- "Rescaling and Definition of δ(xs,w)" --- p.29 / Chapter 2.6 --- An Interior Point Method --- p.32 / Chapter 2.6.1 --- Algorithm with Full Newton Steps --- p.33 / Chapter 2.6.2 --- Iteration Bound --- p.33 / Chapter 2.7 --- Background and Rounding Procedure for Interior-point Solution --- p.36 / Chapter 2.8 --- Solving Some LP problems --- p.42 / Chapter 2.9 --- Remarks --- p.51 / Chapter 3 --- Convex Optimization --- p.53 / Chapter 3.1 --- Introduction --- p.53 / Chapter 3.1.1 --- Convex Optimization Problem --- p.53 / Chapter 3.1.2 --- Idea of Interior Point Method --- p.55 / Chapter 3.2 --- Logarithmic Barrier Method --- p.55 / Chapter 3.2.1 --- Basic Concepts and Properties --- p.55 / Chapter 3.2.2 --- k-Self-Concordance Condition --- p.62 / Chapter 3.2.3 --- Short-step Logarithmic Barrier Algorithm --- p.64 / Chapter 3.2.4 --- Initialization Algorithm --- p.67 / Chapter 3.3 --- Center Method --- p.70 / Chapter 3.3.1 --- Basic Concepts and Properties --- p.70 / Chapter 3.3.2 --- Short-step Center Algorithm --- p.75 / Chapter 3.3.3 --- Initialization Algorithm --- p.76 / Chapter 3.4 --- Properties and Examples on Self-Concordance --- p.78 / Chapter 3.5 --- Examples of Convex Optimization Problem --- p.82 / Chapter 3.5.1 --- Self-concordant Logarithmic Barrier and Distance Function --- p.82 / Chapter 3.5.2 --- General Convex Optimization Problems --- p.91 / Chapter 3.6 --- Remarks --- p.98 / Bibliography
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_322201 |
| Date | January 1998 |
| Contributors | Ng, Shiu-Tung., 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, 103 leaves : ill. ; 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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