非线性半定规划一个全局收敛的无罚无滤子SSDP算法

doi:10.15960/j.cnki.issn.1007-6093.2018.04.001

Operations Research Transactions

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

LI Jianling¹ZHANG Hui¹YANG Zhenping²JIAN Jinbao^3,*

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

Abstract

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

LI Jianling, ZHANG Hui, YANG Zhenping, JIAN Jinbao.

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

[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2018.04.001.

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

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