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Abstract and Applied Analysis
Volume 2014, Article ID 436415, 9 pages
http://dx.doi.org/10.1155/2014/436415
Research Article

A QP-Free Algorithm for Finite Minimax Problems

1College of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
2School of Mathematics and Information Science, Yulin Normal University, Yulin, Guangxi 537000, China
3Guangxi Economic Management Cadre College, Nanning, Guangxi 530007, China

Received 5 April 2014; Accepted 5 June 2014; Published 24 June 2014

Academic Editor: Chong Li

Copyright © 2014 Daolan Han et al. 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

The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided.