求解一类极大极小优化问题的神经网络方法  

A neural network for solving a class of min-max optimization problems

作　　者：沈洁[1] 宋雨徽 陆艳玲 SHEN Jie;SONG Yu-hui;LU Yan-ling(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林师范大学学报（自然科学版）》2023年第3期56-60,共5页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(61877032)。

摘　　要：采用神经网络方法研究了一类极大极小非光滑优化问题.首先利用优化技术和熵函数,将非光滑问题转化为近似的光滑优化问题,再基于最优性条件和投影方法,构建求解近似问题的神经网络模型.不仅证明了给出的神经网络在Lyapunov意义下是稳定的,而且其输出轨线全局收敛到近似问题的最优解.最后的数值仿真例子表明了该方法的有效性.A class of minimax nonsmooth optimization problems was studied by a neural network method.Firstly,the non-smooth problem was transformed into an approximate smooth optimization problem by using optimization technique and entropy function.Then,a neural network model for solving the approximate problem was constructed based on optimality conditions and projection method.It was not only proved that the given neural network was stable in the sense of Lyapunov,but also its output trajectory globally converged to the optimal solution of the approximate problem.Finally,a numerical simulation example showed the effectiveness of the method.

关 键 词：非光滑优化 神经网络 投影算子 收敛性 稳定性 

分 类 号：O221.2[理学—运筹学与控制论]