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Volume 41, Issue 1
A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems

Jinbao Jian, Guodong Ma & Yufeng Zhang

DOI: 10.4208/jcm.2106-m2020-0059

J. Comp. Math., 41 (2023), pp. 133-152.

Published online: 2022-11

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  • Abstract

In this paper, we discuss the nonlinear minimax problems with inequality constraints. Based on the stationary conditions of the discussed problems, we propose a sequential systems of linear equations (SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point. By means of the new working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations (SLE). At each iteration, two  systems of linear equations (SLEs) with the same uniformly nonsingular coefficient matrix are solved. Under mild conditions, the proposed algorithm possesses global and strong convergence. Finally, some preliminary numerical experiments are reported.

  • Keywords

Inequality constraints, Minimax problems, Method of quasi-strongly sub-feasible directions, SSLE-type algorithm, Global and strong convergence.

  • AMS Subject Headings

90C30, 90C47, 65K05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jianjb@gxu.edu.cn (Jinbao Jian)

mgd2006@163.com (Guodong Ma)

1178452540@qq.com (Yufeng Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-133, author = {Jian , JinbaoMa , Guodong and Zhang , Yufeng}, title = {A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {1}, pages = {133--152}, abstract = {

In this paper, we discuss the nonlinear minimax problems with inequality constraints. Based on the stationary conditions of the discussed problems, we propose a sequential systems of linear equations (SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point. By means of the new working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations (SLE). At each iteration, two  systems of linear equations (SLEs) with the same uniformly nonsingular coefficient matrix are solved. Under mild conditions, the proposed algorithm possesses global and strong convergence. Finally, some preliminary numerical experiments are reported.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2106-m2020-0059}, url = {http://global-sci.org/intro/article_detail/jcm/21173.html} }
TY - JOUR T1 - A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems AU - Jian , Jinbao AU - Ma , Guodong AU - Zhang , Yufeng JO - Journal of Computational Mathematics VL - 1 SP - 133 EP - 152 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2106-m2020-0059 UR - https://global-sci.org/intro/article_detail/jcm/21173.html KW - Inequality constraints, Minimax problems, Method of quasi-strongly sub-feasible directions, SSLE-type algorithm, Global and strong convergence. AB -

In this paper, we discuss the nonlinear minimax problems with inequality constraints. Based on the stationary conditions of the discussed problems, we propose a sequential systems of linear equations (SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration point. By means of the new working set, we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations (SLE). At each iteration, two  systems of linear equations (SLEs) with the same uniformly nonsingular coefficient matrix are solved. Under mild conditions, the proposed algorithm possesses global and strong convergence. Finally, some preliminary numerical experiments are reported.

Jian , JinbaoMa , Guodong and Zhang , Yufeng. (2022). A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems. Journal of Computational Mathematics. 41 (1). 133-152. doi:10.4208/jcm.2106-m2020-0059
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