Distributed dual averaging algorithm for multi-agent optimization with coupled constraints

This paper investigates a distributed algorithm for the multi-agent constrained optimization problem, which is to minimize a global objective function formed by a sum of local convex (possibly nonsmooth) functions under both coupled inequality and affine equality constraints.By introducing auxiliary variables, we decouple the constraints and transform the multi-agent optimization problem into a variational inequality problem with a set-valued monotone mapping.We propose a distributed dual averaging algorithm to find the weak solutions of the variational inequality problem with an O(1/ √ k) convergence rate, where k is the number of iterations.Moreover, we show that weak solutions are also strong solutions that match the optimal primal-dual solutions to the considered optimization problem.A numerical example is given for illustration.