摘要
研究一类分布式优化问题,其目标是在满足耦合不等式约束和局部可行集约束的情况下使非光滑全局代价函数值最小.首先,对原有的分布式连续时间投影算法进行拓展,结合线性代数理论分析,设计一个适用于强连通加权平衡有向通信网络拓扑图的算法.其次,在局部代价函数和耦合不等式约束函数是非光滑凸函数的假设条件下,利用Moreau-Yosida函数正则化使目标函数和约束函数近似光滑可微.然后,根据强连通加权平衡有向图的分布式连续时间投影算法构造李雅普诺夫函数,证明该算法下的平衡解是分布式优化问题最优解,并对算法进行收敛性分析.最后,通过数值仿真验证算法的有效性.
In this paper,we study a class of distributed optimization problems whose objective is to minimize the value of a non-smooth global cost function while satisfying the coupling inequality constraint and the local feasible set constraint.First,we extend the original distributed continuous-time projection algorithm with linear algebraic theory analysis to design an algorithm for strongly connected weighted-balanced directed communication network topology graphs.Second,under the assumption that the local cost function and the coupled inequality constraint function are non-smooth convex functions,we use the Moreau-Yosida function regularization to make the objective function and the constraint function approximately smooth and differentiable.Then,the Lyapunov function is con-structed according to the distributed continuous time projection algorithm of the strongly connected weighted equi-librium directed graph,the equilibrium solution under this algorithm is proved to be the optimal solution of the dis-tributed optimization problem,as well as the convergence analysis of the algorithm is performed.Finally,the effect-iveness of the algorithm is verified by numerical simulation.
作者
刘奕葶
马铭莙
付俊
LIU Yi-Ting;MA Ming-Jun;FU Jun(State Key Laboratory of Synthetical Automation for Process Industries,Northeastern University,Shenyang 110819)
出处
《自动化学报》
EI
CAS
CSCD
北大核心
2024年第1期66-75,共10页
Acta Automatica Sinica
基金
国家重点研发计划(2018AAA0101603)资助。
关键词
多智能体网络
分布式优化
加权平衡有向图
耦合不等式约束
Multi-agent networks
distributed optimization
weight-balanced digraphs
coupled inequality con-straints
