Distributed Global Optimization for a Class of Nonconvex Optimization With Coupled Constraints

• 成果类型: Article
• 署名作者: Ren, Xiaoxing; Li, Dewei; Xi, Yugeng; Shao, Haibin
• 署名单位: Shanghai Jiao Tong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3115430
• 发表日期: 2022
• 页码: 4322-4329
• 关键词: Optimization; Signal processing algorithms; linear programming; CONVERGENCE; manganese; Distributed algorithms; Convex functions; Canonical duality; Distributed nonconvex optimization; global optimization; primal-dual method

摘要

This article examines the distributed nonconvex optimization problem with structured nonconvex objective functions and coupled convex inequality constraints on static networks. A distributed continuous-time primal-dual algorithm is proposed to solve the problem. We use the canonical transformation and Lagrange multiplier method to reformulate the nonconvex optimization problem as a convex-concave saddle point computation problem, which is subsequently solved by employing the projected primal-dual subgradient method. Sufficient conditions that guarantee the global optimality of the solution generated by the proposed algorithm are provided. Numerical and application examples are presented to demonstrate the proposed algorithm.