A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems  

作　　者：Jin-bao Jian Ran Quan Qing-jie Hu 

机构地区：[1]College of Mathematics and Information Science, Guangxi University, Nanning 530004, China [2]College of Electrical Engineering, Guangxi University, Nanning 530004, Chin [3]Department of Information, Hunan Business College, Changsha 410205, China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第3期395-410,共16页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.10261001);Guangxi Science Foundation(Nos.0236001,0640001);China as well as Guangxi University Key Program for Science and Technology Research(No.2005ZD02).

摘　　要：In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.

关 键 词：Minimax problems SQP algorithm global convergence superlinear convergence 

分 类 号：O17[理学—数学]