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 - <p style="text-align: justify;">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&nbsp; 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.</p>