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

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.