半定规划的非内点连续化方法(英文)  

Noninterior Continuation Method for Solving Semidefinite Programming

作　　者：乌彩英[1] 陈国庆[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2009年第2期381-390,共10页Mathematica Applicata

基　　金：Supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutes of Ministry of Education

摘　　要：基于Fischer-Burmeister函数,本文将半定规划(SDP)的中心路径条件转化为非线性方程组,进而用SDCP的非内点连续化方法求解之.证明了牛顿方向的存在性,迭代点列的有界性.在适当的假设条件下,得到算法的全局收敛性及局部二次收敛率.数值结果表明算法的有效性.Based on smoothing Fischer-Burmeister function,we reformulate the central path conditions for semidefinite programing （SDP） as a nonlinear system of equations,and then extend the noninterior continuation method from SDCP to this problem. Furthermore,issues such as existence of Newton directions, boundedness of iterates,global convergence and local quadratic convergence of the algorithm will be studied under suitable assumptions. Some numerical results are included.

关 键 词：半定规划 Fischer—Burmeister函数 非内点连续化方法 全局收敛 二次收敛 

分 类 号：O221[理学—运筹学与控制论]