广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (5): 101-109.doi: 10.16088/j.issn.1001-6600.2023110802

• 研究论文 • 上一篇    下一篇

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

黄镘潼, 喻昕*   

  1. 广西大学 计算机与电子信息学院,广西 南宁 530004
  • 收稿日期:2023-11-08 修回日期:2024-02-20 出版日期:2024-09-25 发布日期:2024-10-11
  • 通讯作者: 喻昕(1973—),男,重庆人,广西大学教授,博士,博导。E-mail: yuxin21@126.com
  • 基金资助:
    国家自然科学基金(61862004)

A Neural Network Algorithm Based on Penalty Function Method for Solving Non-smooth Pseudoconvex Optimization Problems and Its Applications

HUANG Mantong, YU Xin*   

  1. School of Computer, Electronics and Information, Guangxi University, Nanning Guangxi 530004, China
  • Received:2023-11-08 Revised:2024-02-20 Online:2024-09-25 Published:2024-10-11

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摘要： 针对实际应用中遇到的非光滑伪凸优化问题,本文提出一种创新的解决方案——结合罚函数理念和微分包含理论的单层神经网络算法。首先,通过数学理论证明,本文算法能够使状态解最终收敛至伪凸优化问题的最优解,从而确立所提出算法的正确性;其次,通过对2个数值实验的模拟收敛结果进行分析,进一步验证算法的有效性;最后,用本文算法解决实际应用问题,展示其在解决伪凸优化问题上的实际应用价值。与现有的神经网络算法相比,本文算法不仅能够解决更一般的具有凸不等式和等式约束的伪凸优化问题,也可以解决实际应用问题。此外,本文算法层次结构简单,无需计算精确的罚参数,可以选取任意初始点,无需添加任何辅助变量,为伪凸优化问题的解决提供一种有效途径。

关键词: 神经网络, 伪凸优化, 最优解, 罚函数, 实际应用

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.

Key words: neural network, pseudoconvex optimization, optimal solution, penalty function, practical application

中图分类号:  TP183

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