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

Authors:
Jin-bao Jian;Ran Quan;Xue-lu Zhang
Affiliations:
College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R. China;College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R. China;College of Mathematics and Information Science, Guangxi University, 530004, Nanning, P.R. China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

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.