非线性半定规划一个新的全局收敛算法  

A New Globally Convergent Algorithm for Nonlinear Semidefinite Programming

作　　者：张辉 黎健玲[1] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁

出　　处：《应用数学进展》2018年第4期456-465,共10页Advances in Applied Mathematics

基　　金：国家自然科学基金(No. 11561005);广西自然科学基金(No. 2016GXNSFAA380248)资助。

摘　　要：本文提出了一个求解非线性半定规划的序列二次半定规划(SSDP)算法。算法每次迭代通过求解两个半定规划子问题确定搜索方向;通过引进距离函数来构造效益函数用于线搜索,从而产生新的迭代点。在适当的假设条件下,算法或收敛到问题的不可行稳定点,或收敛到问题的KKT点。In this paper, we present a sequence quadratic semidefinite programming (SSDP) algorithm for nonlinear semidefinite programming. At each iteration, the search direction is determined by solving two semidefinite programming sub problems;by introducing a distance function, a merit function is constructed for line search. Under some appropriate conditions, any accumulation point of iterative point sequence is either an infeasible stationary point, or a KKT point of the problem.

关 键 词：非线性半定规划 SSDP算法 KKT点 全局收敛性 

分 类 号：O22[理学—运筹学与控制论]