广西师范大学学报（自然科学版）2024，Vol.42Issue(5)：101-109,9.DOI:10.16088/j.issn.1001-6600.2023110802
一种基于罚函数法解决非光滑伪凸优化问题的神经网络算法及其应用
A Neural Network Algorithm Based on Penalty Function Method for Solving Non-smooth Pseudoconvex Optimization Problems and Its Applications
摘要
Abstract
To address the nonsmooth pseudoconvex optimization problems encountered in practical applications,an innovative solution is proposed:a single-layer neural network algorithm that integrates the concept of penalty functions and the theory of differential inclusions.Firstly,through mathematical theory,it is proved that this algorithm can ensure that the state solutions ultimately converge to the optimal solution of the pseudoconvex optimization problem,thus establishing the correctness of the proposed algorithm.Secondly,the effectiveness of the algorithm is further verified through the analysis of simulated convergence results from two numerical experiments.Finally,the applications of this algorithm to practical problems demonstrate its practical application value in solving pseudoconvex optimization issues.Compared with existing neural network algorithms,this algorithm can not only solve more general pseudoconvex optimization problems with convex inequality and equality constraints but also tackle practical application issues.Moreover,the algorithm has a simple hierarchical structure,does not require the calculation of precise penalty parameters,allows for the selection of any starting point,and does not add any auxiliary variable,which thus provides an effective approach to solving pseudoconvex optimization problems.关键词
神经网络/伪凸优化/最优解/罚函数/实际应用Key words
neural network/pseudoconvex optimization/optimal solution/penalty function/practical application分类
信息技术与安全科学引用本文复制引用
黄镘潼,喻昕..一种基于罚函数法解决非光滑伪凸优化问题的神经网络算法及其应用[J].广西师范大学学报（自然科学版）,2024,42(5):101-109,9.基金项目
国家自然科学基金(61862004) （61862004）
