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The Scientific World Journal
Volume 2014, Article ID 159754, 9 pages
http://dx.doi.org/10.1155/2014/159754
Research Article

A Simple SQP Algorithm for Constrained Finite Minimax Problems

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

Received 30 August 2013; Accepted 7 November 2013; Published 10 February 2014

Academic Editors: Z.-C. Deng, K. Skouri, and K.-C. Ying

Copyright © 2014 Lirong Wang and Zhijun Luo. 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

A simple sequential quadratic programming method is proposed to solve the constrained minimax problem. At each iteration, through introducing an auxiliary variable, the descent direction is given by solving only one quadratic programming. By solving a corresponding quadratic programming, a high-order revised direction is obtained, which can avoid the Maratos effect. Furthermore, under some mild conditions, the global and superlinear convergence of the algorithm is achieved. Finally, some numerical results reported show that the algorithm in this paper is successful.