Distributed Nonsmooth Consensus Optimization Problems with Coupled Inequality Constraint: A Proximal Approach

Distributed nonsmooth consensus optimization problems with the coupled inequality constraint are investigated in this paper. The global objective consists of convex and nonsmooth local cost functions. Each agent has only the information of its corresponding local cost function. Moreover, the coupled inequality constraint and consensus constraint are also considered. By employing the proximal method, a distributed proximal-gradient algorithm is proposed. The convergence result is theoretically analysed by using Lyapunov stability theory. It shows that the multi-agent system driven by the proposed algorithm can reach consensus and satisfy the coupled equality constraint at the optimal solution. In the end, the results of the simulation show the efficiency of the proposed algorithm.