半定规划的PRP^＋共轭梯度法(英文)  

PRP^+ Conjugate Gradient 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》2010年第2期384-391,共8页Mathematica Applicata

基　　金：Supported by Program of Higher-level Talents of Inner Mongolia University(Z20090135)

摘　　要：本文对半定规划(SDP)的最优性条件提出一价值函数并研究其性质.基此,提出半定规划的PRP+共轭梯度法.为得到PRP+共轭梯度法的收敛性,提出一Armijo-型线搜索.无需水平集有界及迭代点列聚点的存在,算法全局收敛.In this paper,a merit function for the optimality conditions of semidefinite programming （SDP） is proposed and related desirable properties are investigated.Based on this merit function,a PRP＋ conjugate gradient method with a new Armijo-type line search for solving （SDP） is presented.The global convergence of the algorithm is proved without requiring the boundedness of level set and existence of accumulation point of produced sequence by the method.

关 键 词：半定规划 价值函数 全局收敛 FISCHER-BURMEISTER函数 

分 类 号：O221[理学—运筹学与控制论]