Composite Optimization With Coupling Constraints via Penalized Proximal Gradient Method in Asynchronous Networks

In this article, we consider a composite optimization problem with linear coupling constraints in a multiagent 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 nonsmooth 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, 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.