求解带有混合约束的极大极小优化问题的神经网络方法  

A neural network for solving min-max optimization problems with mixed constrains

作　　者：沈洁[1] 解昱菲 郑欣蕾 SHEN Jie;XIE Yufei;ZHENG Xinlei(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2023年第4期433-437,共5页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61877032)。

摘　　要：通过构建神经网络求解极大极小非光滑优化问题.主要利用光滑的熵函数近似非光滑目标函数,将问题转化为光滑优化问题,进而根据KKT条件构建神经网络模型.我们证明了构建的神经网络模型在Lyapunov意义下是稳定的,并收敛到极大极小问题的近似最优解.最后的数值实验证明了方法的有效性.In this paper, a neural network is constructed to solve min-max non-smooth optimization problem. The smooth entropy function is mainly used to approximate the non-smooth objective function, and the problem is transformed into a smooth optimization problem, and then the neural network model is constructed according to the KKT condition. We show that the constructed neural network model is stable in the sense of Lyapunov and converges to the approximate optimal solution of the min-max problem. Finally, numerical experiments demonstrate the effectiveness of the method.

关 键 词：极大极小优化 神经网络模型 熵函数 LYAPUNOV函数 稳定性 

分 类 号：O221.2[理学—运筹学与控制论]