递归神经网络方法解决非光滑伪凸优化问题  

RECURRENT NEURAL NETWORK METHOD FOR SOLVING NONSMOOTH PSEUDOCONVEX OPTIMIZATION PROBLEMS

作　　者：喻昕[1] 胡悦[1] 马崇[1] 伍灵贞 汪炎林 Yu Xin;Hu Yue;Ma Chong;Wu Lingzhen;Wang Yanlin(School of Computer and Electronics Information,Guangxi University,Nanning 530004,Guangxi,China)

机构地区：[1]广西大学计算机与电子信息学院

出　　处：《计算机应用与软件》2019年第11期145-151,242,共8页Computer Applications and Software

基　　金：国家自然科学基金项目(61462006,61862004)

摘　　要：针对目标函数为非光滑伪凸函数且带有等式约束和不等式约束的优化问题,基于罚函数以及微分包含的思想,构建一个层次仅为一层且不包含惩罚算子的新型递归神经网络模型.该模型不用提前计算惩罚参数,能够很好地收敛.理论证明全局解存在,模型的状态解能够在有限的时间内进到原目标函数的可行域并不再离开,其状态解最终收敛到目标函数的一个最优解.仿真实验证实了理论结果的可行性.Aiming at the optimization problem of nonsmooth pseudoconvex function with equality and inequality constraints,a new recursive neural network model with only one level and no penalty operator is constructed based on the idea of penalty function and differential inclusion.The model did not need to calculate penalty parameters in advance and could converge well.We theoretically prove the existence of global solutions.The state solutions of the model can enter the feasible region of the original objective function in a limited time and never leave,and the state solutions of the model converge to an optimal solution of the objective function.The feasibility of the theoretical results is verified by simulation experiments.

关 键 词：递归神经网络 非光滑伪凸优化 收敛性 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]