Composite optimization with coupling constraints via penalized proximal gradient method in asynchronous networks

• Main Authors: Wang, Jianzheng, Hu, Guoqiang
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2023
• Subjects: Engineering::Electrical and electronic engineering; Multi-Agent Network; Composite Optimization
• Online Access: https://hdl.handle.net/10356/170708
• Institution: Nanyang Technological University

In this paper, we consider a composite optimization problem with linear coupling constraints in a multi-agent network. In this problem, the agents cooperatively optimize a strongly convex cost function which is the linear sum of individual cost functions composed of smooth and possibly non-smooth components. To solve this problem, we propose an asynchronous penalized proximal gradient (Asyn-PPG) algorithm, a variant of classical proximal gradient method, with the presence of the asynchronous updates of the agents and uniform communication delays in the network. Specifically, we consider a slot-based asynchronous network (SAN), where the whole time domain is split into sequential time slots and each agent is permitted to execute multiple updates during a slot by accessing the historical state information of the agents. By the Asyn-PPG algorithm, an explicit convergence rate can be guaranteed based on deterministic analysis. The feasibility of the proposed algorithm is verified by solving a consensus-based distributed regression problem and a social welfare optimization problem in the electricity market.