Distributed Nonsmooth Optimization with Consensus and Inequality Constraints via Distributed Smooth Proximal-Splitting Algorithm

This paper investigates a class of distributed nonsmooth optimization problems with consensus and inequality constraints. Each local cost function contains a smooth convex function and two nonsmooth convex functions. Moreover, consensus needs to be achieved at the optimal solution of these problems. With the help of splitting method, a distributed smooth proximal-splitting algorithm is proposed in this paper. The convergence analysis of this algorithm is conducted by employing Lyapunov stability theory and the property of proximal operator. Combining with simulation results, it is shown that the multi-agent system steered by the proposed algorithm can reach consensus on the optimal point while satisfying inequality constraints.