Interior point method for linear and convex optimizations.

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.5Chapter 1.1 --- Linear and Convex Optimization Model --- p.5Chapter 1.2 --- Notations for Linear Optimization --- p.5Chapter 1.3 --- Definition and Properties of Convexities --- p.7Chapter 1.4 --- Useful Theorem for Unconstrained Minimization --- p.10Chapter 2 --- Linear Optimization --- p.11Chapter 2.1 --- Self-dual Linear Optimization Model --- p.11Chapter 2.2 --- Definitions and Main Theorems --- p.14Chapter 2.3 --- Self-dual Embedding and Simple Example --- p.22Chapter 2.4 --- Newton step --- p.25Chapter 2.5 --- "Rescaling and Definition of δ(xs,w)" --- p.29Chapter 2.6 --- An Interior Point Method --- p.32Chapter 2.6.1 --- Algorithm with Full Newton Steps --- p.33Chapter 2.6.2 --- Iteration Bound --- p.33Chapter 2.7 --- Background and Rounding Procedure for Interior-point Solution --- p.36Chapter 2.8 --- Solving Some LP problems --- p.42Chapter 2.9 --- Remarks --- p.51Chapter 3 --- Convex Optimization --- p.53Chapter 3.1 --- Introduction --- p.53Chapter 3.1.1 --- Convex Optimization Problem --- p.53Chapter 3.1.2 --- Idea of Interior Point Method --- p.55Chapter 3.2 --- Logarithmic Barrier Method --- p.55Chapter 3.2.1 --- Basic Concepts and Properties --- p.55Chapter 3.2.2 --- k-Self-Concordance Condition --- p.62Chapter 3.2.3 --- Short-step Logarithmic Barrier Algorithm --- p.64Chapter 3.2.4 --- Initialization Algorithm --- p.67Chapter 3.3 --- Center Method --- p.70Chapter 3.3.1 --- Basic Concepts and Properties --- p.70Chapter 3.3.2 --- Short-step Center Algorithm --- p.75Chapter 3.3.3 --- Initialization Algorithm --- p.76Chapter 3.4 --- Properties and Examples on Self-Concordance --- p.78Chapter 3.5 --- Examples of Convex Optimization Problem --- p.82Chapter 3.5.1 --- Self-concordant Logarithmic Barrier and Distance Function --- p.82Chapter 3.5.2 --- General Convex Optimization Problems --- p.91Chapter 3.6 --- Remarks --- p.98Bibliograph