一种解决受约束的非光滑伪凸优化问题的新型神经网络方法  

New Neural Network Method for Solving Nonsmooth Pseudoconvex Optimization Problems with Constraints

作　　者：喻昕[1,2] 伍灵贞 汪炎林 YU Xin;WU Ling-zhen;WANG Yan-lin(Department of Computer and Electronic Information,Guangxi University,Nanning 530004,China;Guangxi Key Laboratory of Multimedia Communications and Network Technology,Nanning 530004,China)

机构地区：[1]广西大学计算机与电子信息学院,南宁530004 [2]广西多媒体通信与网络技术重点实验室,南宁530004

出　　处：《小型微型计算机系统》2020年第3期544-550,共7页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61862004,61462006)资助.

摘　　要：非光滑伪凸优化问题涉及科学与工程应用的诸多领域,是非光滑凸优化问题的扩展,同时也是一种特殊的非凸优化问题,具有十分重要的研究价值.针对这类问题,提出了一种基于微分包含的新型神经网络模型,用来解决带有等式与不等式约束的非光滑伪凸优化问题.通过严谨的理论分析证明新型神经网络的轨迹可以在有限时间内进入到可行域,且最终会收敛于原始优化问题的最优解,最后通过仿真实验的方式验证新型神经网络的有效性与准确性.与现有神经网络相比,新型神经网络具有以下优势:避免预先计算任何的精确惩罚因子,降低计算复杂度;初始点可以取实数空间任意有效值,不受限制;模型结构相对简单.Nonsmooth pseudoconvex optimization problem involves many fields of science and engineering application. It is not only an extension of nonsmooth convex optimization problem,but also a special nonconvex optimization problem. It has very important research value. To solve these problems,a new neural network method based on differential inclusion is proposed to solve the nonsmooth pseudoconvex optimization problem with equality and inequality constraints. Through rigorous theoretical analysis,it is proved that the trajectory of the new neural network can enter the feasible region in a limited time,and eventually converge to the optimal solution of the original optimization problem. And then,the effectiveness and accuracy of the new neural network are verified by simulation experiments.Compared with the existing neural networks,the new neural network has the following advantages: avoiding any exact penalty factor in advance and reducing the computational complexity;the initial point can take any real space effective value without restriction;the structure of the model is relatively simple.

关 键 词：神经网络 伪凸优化问题 收敛 最优解 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]