一种基于神经动力学解决伪凸优化问题的分布式算法  

Distributed Approach Based on Neurodynamics to Solve Pseudoconvex Optimization Problem

作　　者：喻昕[1] 李浩宇 YU Xin;LI Haoyu(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》2025年第3期594-601,共8页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61862004)资助.

摘　　要：伪凸优化作为非凸优化中的一个重要问题,在现代工程领域占有重要的地位.该文提出一种基于投影法及惩罚方法的神经动力学方法,求解具有不等式约束及等式约束的分布式伪凸优化问题.相较于已存在的各类算法,本文提出的算法在分布式系统中提高了各智能体间通信的效率,仅使用涉及系统决策的状态变量进行相互通信,因此能够节省大量通信资源.本文基于非光滑分析和Lyapunov理论,证明了网络系统中的所有智能体的状态变量在有限时间内进入可行域内并永驻其中,并且可以在有限时间内达成一致,然后渐近收敛到所考虑的优化问题的最优解.同时给出了两个数值实验的仿真结果,验证了本文所提出的算法的有效性.As an important problem in non-convex optimization,pseudoconvex optimization occupies an important position in the field of modern engineering.In this paper,a neurodynamic method based on the projection method and the penalty method is proposed to solve distributed pseudoconvex optimization problems with equation and inequality constraints.Compared with the existing algorithms,the algorithm proposed in this paper improves the communication efficiency between agents in the distributed system,and only uses the state variables involved in the system decision to communicate with each other,so it can save a lot of communication resources.Based on non-smooth analysis and Lyapunov theory,this paper shows that the state variables of all agents in the network system entry the feasible domain in a finite time and stay in it forever,and can reach agreement in a finite time,and then converge to the optimal solution of the optimization problem under consideration.At the same time,the simulation results of two numerical experiments are given,which verifies the effectiveness of the proposed algorithm.

关 键 词：分布式优化 伪凸优化 神经动力学 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]