Penalty Function-Based Distributed Primal-Dual Algorithm for Nonconvex Optimization Problem

作     者：Xiasheng Shi Changyin Sun 

作者机构：IEEE the Engineering Research Center of Autonomous Unmanned System Technology Ministry of Education Anhui University the School of Artificial Intelligence Anhui University Anhui Provincial Engineering Research Center for Unmanned System and Intelligent Technology Anhui University the Anhui Key Laboratory Industrial Energy-Saving and Safety Anhui University 

出 版 物：《IEEE/CAA Journal of Automatica Sinica》 (自动化学报(英文版))

年 卷 期：2025年第12卷第2期

页      面：394-402页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：supported in part by the National Natural Science Foundation of China (62236002, 62403004, 62203001, 62303009,62136008) the Open Project of Anhui Key Laboratory of Industrial Energy-Saving and Safety,Anhui University (KFKT202405) 

主　　题：Constrained optimization Karush-Kuhn-Tucker (KKT) point nonconvex p-power transformation 

摘      要：This paper addresses the distributed nonconvex optimization problem, where both the global cost function and local inequality constraint function are nonconvex. To tackle this issue, the p-power transformation and penalty function techniques are introduced to reframe the nonconvex optimization problem. This ensures that the Hessian matrix of the augmented Lagrangian function becomes local positive definite by choosing appropriate control parameters. A multi-timescale primal-dual method is then devised based on the Karush-Kuhn-Tucker(KKT) point of the reformulated nonconvex problem to attain convergence. The Lyapunov theory guarantees the model s stability in the presence of an undirected and connected communication network. Finally, two nonconvex optimization problems are presented to demonstrate the efficacy of the previously developed method.