Convergence Analysis of an Inexact Feasible Interior Point Method for Convex Quadratic Programming

In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields a short-step algorithm and a symmetric one induced by the use of the infinity norm which yields a (practical) long-step algorithm. Both algorithms allow for the Newton equation system to be solved inexactly. For both algorithms we will provide conditions for the level of error acceptable in the Newton equation and establish the worst-case complexity results

On implementation of a self-dual embedding method for convex programming.

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.1Chapter 2 --- Background --- p.7Chapter 2.1 --- Self-dual embedding --- p.7Chapter 2.2 --- Conic optimization --- p.8Chapter 2.3 --- Self-dual embedded conic optimization --- p.9Chapter 2.4 --- Connection with convex programming --- p.11Chapter 2.5 --- Chapter summary --- p.15Chapter 3 --- Implementation of the algorithm --- p.17Chapter 3.1 --- The new search direction --- p.17Chapter 3.2 --- Select the step-length --- p.23Chapter 3.3 --- The multi-constraint case --- p.25Chapter 3.4 --- Chapter summary --- p.32Chapter 4 --- Numerical results on randomly generated problem --- p.34Chapter 4.1 --- Single-constraint problems --- p.35Chapter 4.2 --- Multi-constraint problems --- p.36Chapter 4.3 --- Running time and the size of the problem --- p.39Chapter 4.4 --- Chapter summary --- p.42Chapter 5 --- Geometric optimization --- p.45Chapter 5.1 --- Geometric programming --- p.45Chapter 5.1.1 --- Monomials and posynomials --- p.45Chapter 5.1.2 --- Geometric programming --- p.46Chapter 5.1.3 --- Geometric program in convex form --- p.47Chapter 5.2 --- Conic transformation --- p.48Chapter 5.3 --- Computational results of geometric optimization problem --- p.50Chapter 5.4 --- Chapter summary --- p.55Chapter 6 --- Conclusion --- p.5