一种解决带有凸集约束的分布式伪凸优化的连续时间算法  

Continuous-time Algorithm for Distributed Pseudoconvex Optimization with Convex Constraint Sets

作　　者：喻昕[1] 王思鉴 YU Xin;WANG Sijian(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》2024年第7期1608-1614,共7页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(61862004)资助。

摘　　要：本文提出了一种可以解决带有凸集约束且全局目标函数是非光滑伪凸的分布式优化问题的连续时间算法.本文所提出的分布式优化算法采用罚函数方法建模,通过构造一个合适的惩罚项迫使所有智能体的状态变量进入可行域.通过使用李雅普诺夫(有限时间)稳定性理论等工具,证明了在一定假设下,本文所提出的算法将在有限时间内达成一致状态且进入可行域并永驻其中,并在此之后收敛到原分布式优化问题的最优解集.此外,该算法在运行时各个智能体仅仅需要接收邻居节点的相对状态的符号信息.最后,仿真结果验证了本文所提出的算法的有效性.This paper develops a continuous-time algorithm model for solving distributed pseudoconvex optimization problems with convex constraint sets.Based on the penalty function method,this paper constructed a suitable penalty term to force the state solution of all agents into the feasible region.Through Lyapunov’s finite-time stability theory,it is proven that under certain assumptions,each state solution will enter the inequality feasible region stay there thereafter,and reach consensus in finite time.Moreover,each solution is convergent to the optimal solution set of the primal distributed optimization problem.In addition,when the algorithm is running,each agent only needs to receive the sign of relative state information.Finally,numerical experiments show the proposed algorithm is effective.

关 键 词：分布式优化 伪凸优化 多智能体系统 罚函数方法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]