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非线性半定规划一个全局收敛的无罚无滤子SSDP算法

黎健玲1  张辉1  杨振平2  简金宝3,*   

  1. 1. 广西大学数学与信息科学学院, 南宁 530004; 2. 上海大学管理学院, 上海 200444; 3. 广西民族大学理学院, 南宁 530006
  • 收稿日期:2018-02-01 出版日期:2018-12-15 发布日期:2018-12-15
  • 通讯作者: 简金宝 E-mail: jianjb@gxu.edu.cn
  • 基金资助:

    国家自然科学基金(No.11561005), 广西自然科学基金(Nos. 2016GXNSFAA380248, 2014GXNSFFA118001)

A globally convergent SSDP algorithm without a penalty function or a filter for nonlinear semidefinite programming

LI Jianling1  ZHANG Hui1  YANG Zhenping2  JIAN Jinbao3,*   

  1. 1. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China; 2. School of Management, Shanghai University, Shanghai 200444, China; 3. College of Science, Guangxi University for Nationalities, Nanning 530006, China
  • Received:2018-02-01 Online:2018-12-15 Published:2018-12-15

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摘要：

提出了一个求解非线性半定规划的无罚函数无滤子序列二次半定规划(SSDP)算法. 算法每次迭代只需求解一个二次半定规划子问题确定搜索方向; 非单调线搜索保证目标函数或约束违反度函数的充分下降, 从而产生新的迭代点. 在适当的假设条件下, 证明了算法的全局收敛性. 最后给出了初步的数值实验结果.

关键词: 非线性半定规划, SSDP算法, 非单调线搜索, 全局收敛性

Abstract:

In this paper, we present a sequence quadratic semidefinite programming (SSDP) algorithm method without a penalty function or a filter for nonlinear  semidefinite programming. At each iteration, the search direction is determined by solving a specially quadratic semidefinite programming subproblem. The nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. The proposed algorithm is globally convergent under some mild conditions. The preliminary numerical results are reported at the end of the paper.

Key words: nonlinear semidefinite programming, SSDP algorithm, nonmonotone line search, global convergence