Non-interior Continuation Algorithm for Solving System of Inequalities over Symmetric Cones

作     者：张颖 卢楠 ZHANG Ying,LU Nan(School of Sciences,Tianjin University,Tianjin 300072,China)

作者机构：School of SciencesTianjin University 

出 版 物：《Transactions of Tianjin University》 (天津大学学报（英文版）)

年 卷 期：2011年第17卷第2期

页      面：89-95页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by National Natural Science Foundation of China (No.10871144) the Seed Foundation of Tianjin University (No.60302023) 

主　　题：system of inequalities symmetric cone non-interior continuation algorithm global linear convergence local quadratic convergence 

摘      要：As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization *** this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric *** is shown that the proposed algorithm is globally convergent and ***,it can start from any point and only needs to solve one system of linear equations at most at each *** suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan *** results indicate that the algorithm is *** systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 *** average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random *** seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones ***,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.