Feasible generalized monotone line search SQP algorithm for nonlinear minimax problems with inequality constraints

In this paper, the nonlinear minimax problems with inequality constraints are discussed, and a sequential quadratic programming (SQP) algorithm with a generalized monotone line search is presented. At each iteration, a feasible direction of descent is obtained by solving a quadratic programming (QP). To avoid the Maratos effect, a high order correction direction is achieved by solving another QP. As a result, the proposed algorithm has global and superlinear convergence. Especially, the global convergence is obtained under a weak Mangasarian–Fromovitz constraint qualification (MFCQ) instead of the linearly independent constraint qualification (LICQ). At last, its numerical effectiveness is demonstrated with test examples.