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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 293475, 7 pages
http://dx.doi.org/10.1155/2014/293475
Research Article

Improved Filter-SQP Algorithm with Active Set for Constrained Minimax Problems

1The Department of Mathematics and Econometrics, Hunan University of Humanities, Science and Technology, Loudi 417000, China
2The Department of Information Science and Engineering, Hunan University of Humanities, Science and Technology, Loudi 417000, China

Received 15 March 2014; Revised 19 July 2014; Accepted 25 August 2014; Published 2 September 2014

Academic Editor: Kazutake Komori

Copyright © 2014 Zhijun Luo and Lirong Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An improved filter-SQP algorithm with active set for constrained finite minimax problems is proposed. Firstly, an active constraint subset is obtained by a pivoting operation procedure. Then, a new quadratic programming (QP) subproblem is constructed based on the active constraint subset. The main search direction is obtained by solving this (QP) subproblem which is feasible at per iteration point and need not to consider the penalty function by using the filter technique. Under some suitable conditions, the global convergence of our algorithm is established. Finally, some numerical results are reported to show the effectiveness of the proposed algorithm.