IJPAM: Volume 35, No. 2 (2007)

A MODIFIED LAGRANGIAN FUNCTION ALGRITHM FOR
MINIMAX PROBLEMS WITH INEQUALITY CONSTRAINTS

Su-Xiang He$^1$, Yan-Li Zhao$^2$
$^1$School of Science
Wuhan University of Technology
Wuhan, 430070, P.R. CHINA
e-mail: suxianghe@163.com
$^2$Wuhan National Laboratory for Optoelectronics
Huazhong University of Science and Technology
Wuhan, 430074, P.R. CHINA
e-mail: wtdzhaoyl@163.com


Abstract.A modified Lagrangian function (MLF) algorithm for solving minimax problems with inequality constraints, is presented. The algorithm alternatively minimizes the MLF in the primal space, and updates the Lagrange multipliers and controlling parameter. Under the mild conditions, the MLF algorithm is shown to converge Q-superlinearly and the error bounds of solution is also established. Finally the numerical results for several problems are reported.

Received: December 27, 2006

AMS Subject Classification: 90C47, 49K35

Key Words and Phrases: modified Lagrangian function algorithm, minimax problems, inequality constraints, numerical results

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2