A Distributed Dual Proximal Algorithm for Non-Smooth Composite Constrained Optimization and Its Application

Distributed optimization is a promising prospect that shows high potential in various applications, such as machine learning, power systems and others. This paper studies a class of constrained composite optimization problems over a network of agents, in which the local cost functions that are privately maintained by agents can be split into a strongly convex term and a convex (or possibly non-smooth) one. To tackle this problem in a distribute manner, a class of synchronous distributed algorithms based on dual proximal methods (SynDis-DuPro) is presented, and its asynchronous version (AsynDis-DuPro) without the global clock is developed as well. Under the proposed schemes, each agent in the network not only possesses the individual step-sizes, but also conducts local computation and communication without leaking its private information. In addition, the practicability and effectiveness of the proposed algorithms are demonstrated by the simulations on distributed energy resources coordination (DERC) based on power systems.