数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1723-1738.doi: 10.1007/s10473-020-0608-5

• 论文 • 上一篇    下一篇

A GLOBALLY CONVERGENT QP-FREE ALGORITHM FOR INEQUALITY CONSTRAINED MINIMAX OPTIMIZATION

简金宝1, 马国栋2   

  1. 1. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, China;
    2. School of Mathematics and Statistics, Yulin Normal University, Yulin 537000, China
  • 收稿日期:2019-08-02 修回日期:2020-07-15 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Guodong MA,E-mail:mgd2006@163.com E-mail:mgd2006@163.com
  • 作者简介:Jinbao JIAN,E-mail:jianjb@gxu.edu.cn
  • 基金资助:
    This work was supported by the Natural Science Foundation of Guangxi Province (2018GXNSFAA281099), the National Natural Science Foundation of China (11771383) and the Yulin Normal University Research Grant (2019YJKY16).

A GLOBALLY CONVERGENT QP-FREE ALGORITHM FOR INEQUALITY CONSTRAINED MINIMAX OPTIMIZATION

Jinbao JIAN1, Guodong MA2   

  1. 1. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, China;
    2. School of Mathematics and Statistics, Yulin Normal University, Yulin 537000, China
  • Received:2019-08-02 Revised:2020-07-15 Online:2020-12-25 Published:2020-12-30
  • Contact: Guodong MA,E-mail:mgd2006@163.com E-mail:mgd2006@163.com
  • Supported by:
    This work was supported by the Natural Science Foundation of Guangxi Province (2018GXNSFAA281099), the National Natural Science Foundation of China (11771383) and the Yulin Normal University Research Grant (2019YJKY16).

摘要: Although QP-free algorithms have good theoretical convergence and are effective in practice, their applications to minimax optimization have not yet been investigated. In this article, on the basis of the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints. By means of a new and much tighter working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix. At each iteration, to obtain the search direction, two reduced systems of linear equations with the same coefficient are solved. Under mild conditions, the proposed algorithm is globally convergent. Finally, some preliminary numerical experiments are reported, and these show that the algorithm is promising.

关键词: minimax optimization, inequality constraints, QP-free algorithm, global convergence

Abstract: Although QP-free algorithms have good theoretical convergence and are effective in practice, their applications to minimax optimization have not yet been investigated. In this article, on the basis of the stationary conditions, without the exponential smooth function or constrained smooth transformation, we propose a QP-free algorithm for the nonlinear minimax optimization with inequality constraints. By means of a new and much tighter working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix. At each iteration, to obtain the search direction, two reduced systems of linear equations with the same coefficient are solved. Under mild conditions, the proposed algorithm is globally convergent. Finally, some preliminary numerical experiments are reported, and these show that the algorithm is promising.

Key words: minimax optimization, inequality constraints, QP-free algorithm, global convergence

中图分类号: 

  • 49K35