Dynamical Primal-Dual Nesterov Accelerated Method and Its Application to Network Optimization

• 成果类型: Article
• 署名作者: Zeng, Xianlin; Lei, Jinlong; Chen, Jie
• 署名单位: Beijing Institute of Technology; Tongji University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3152720
• 发表日期: 2023
• 页码: 1760-1767
• 关键词: Continuous-time algorithm; Nesterov's accelerated method; network optimization; primal-dual method

摘要

This article develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This article analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is O( 1/t(2)) by choosing suitable parameters. As far as we know, this is the first continuous-time primaldual accelerated method that can obtain the optimal rate. Then, this article applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.