A Large-update Interior-point Algorithm for Convex Quadratic Semi-definite Optimization Based on a New Kernel Function

作     者：Ming Wang ZHANG 

作者机构：College of ScienceChina Three Gorges University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2012年第28卷第11期

页      面：2313-2328页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Natural Science Foundation of Hubei Province of China (Grant No. 2008CDZ047) 

主　　题：Convex quadratic semi-definite optimization kernel function interior-point algorithm^large-update method complexity 

摘      要：In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be O（√n（logn）2 log e/n）. This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and in optimization fields. Some computational results recent kernel functions introduced by some authors have been provided.