A generalized neural network for solving a class of minimax optimization problems with linear constraints

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• 作者：Yongqing Yang^a ; ^{yyq640613@gmail.com} ; ^{yongqingyang@163.com} ; Jinde Cao^b ; ^{jdcao@seu.edu.cn} ; Xianyun Xu^a ; Jiao Liu^a
• 关键词：Minimax optimization ; Differential inclusions ; Neural network ; Convergence
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 March, 2012
• 卷：218
• 期：14
• 页码：7528-7537
• 文件大小：865 K

摘要

In this paper, a generalized neural network was proposed based on projection method and differential inclusions, which is contributed to solve a class of minimax optimization problems with linear constraints. It is proved that the solution trajectory can converge to the feasible region in the finite time when the initial point is not in the feasible region. Once the solution trajectory reaches the feasible region, it will stay therein thereafter. In addition, we investigate the global convergence and exponential convergence. Furthermore, three illustrative examples are given to show the efficiency of the proposed neural network.