A SSLE-Type Algorithm of Quasi-Strongly Sub-Feasible Directions for Inequality Constrained Minimax Problems

Authors

  • Jinbao Jian College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi University for Nationalities, Nanning 530006, China
  • Guodong Ma College of Mathematics and Physics, Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Center for Applied Mathematics and Artificial Intelligence, Guangxi University for Nationalities, Nanning 530006, China
  • Yufeng Zhang School of Mathematics and Information Science, Guangxi University, Nanning 530004, China

DOI:

https://doi.org/10.4208/jcm.2106-m2020-0059

Keywords:

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

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.

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Published

2022-12-01

Issue

Vol. 41 No. 1 (2023)

Section

Articles