| A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems |
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| 作者姓名： | Jin-bao Jian Ran Quan Qing-jie Hu |
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| 作者单位： | [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 |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10261001） and Guangxi Science Foundation （Nos. 0236001, 0640001） of China as well as Guangxi University Key Program for Science and Technology Research （No. 2005ZD02）. |
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| 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.
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| 关 键 词： | 极值问题 计算方法 超线形函数 数学 |
| 收稿时间： | 8 May 2005 |
| 修稿时间： | 2005-05-082007-03-13 |
A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems |
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| Jin-bao Jian Ran Quan Qing-jie Hu.A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems[J].Acta Mathematicae Applicatae Sinica,2007,23(3):395-410. |
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| Authors: | Jin-bao Jian Ran Quan Qing-jie Hu |
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| Institution: | (1) College of Mathematics and Information Science, Guangxi University, Nanning, 530004, China;(2) College of Electrical Engineering, Guangxi University, Nanning, 530004, China;(3) Department of Information, Hunan Business College, Changsha, 410205, China |
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| Abstract: | Abstract
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.
Supported by the National Natural Science Foundation of China (No. 10261001) and Guangxi Science Foundation (Nos. 0236001,
0640001) of China as well as Guangxi University Key Program for Science and Technology Research (No. 2005ZD02). |
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| Keywords: | Minimax problems SQP algorithm global convergence superlinear convergence |
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