Projected Primal-Dual Dynamics for Distributed Constrained Nonsmooth Convex Optimization

作     者：Zhu, Yanan Yu, Wenwu Wen, Guanghui Chen, Guanrong 

作者机构：Southeast Univ Sch Math Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3000 Australia City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China 

出 版 物：《IEEE TRANSACTIONS ON CYBERNETICS》 (IEEE Trans. Cybern.)

年 卷 期：2020年第50卷第4期

页      面：1776-1782页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [61673107, 61673104] National Ten Thousand Talent Program for Young Top-Notch Talents [W2070082] General Joint Fund of the Equipment Advance Research Program of Ministry of Education [6141A020223] Jiangsu Provincial Key Laboratory of Networked Collective Intelligence [BM2017002] Natural Science Foundation of Jiangsu Province of China [BK20170079] Hong Kong Research Grants Council through GRF [CityU 11234916] 

主　　题：Optimization Convex functions Heuristic algorithms Linear programming Convergence Cybernetics Indexes Distributed convex optimization multiagent networks nonsmooth analysis primal-dual dynamics 

摘      要：A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal-dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle s invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal-dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal-dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results.