A Distributed Proximal-Based Primal-Dual Algorithm for Composite Optimization with Coupled Constraints

Abstract

This paper studies a class of distributed convex optimization problems subject to coupled equality and inequality constraints, which are affine and convex functions respectively. The objective is to minimize the sum of a strongly convex smooth function and two convex nonsmooth functions. For such a composite optimization problem with coupled constraints, we propose a distributed proximal-based primal-dual (DPPD) algorithm with a fixed stepsize, based on operators splitting technique and dual decomposition method, where an auxiliary variable is introduced to evict the unproximal characteristics of complex nonsmooth functions. Via Lyapunov stability theory, it is proved that global optimal solution is obtained with an $O\left( {\frac{1}{t}} \right)$ convergence rate. Finally, the theoretical results are demonstrated in an economic dispatch (ED) problem.