Distributed convex nonsmooth optimization for multi-agent system based on proximal operator

This paper considers a class of distributed non-differentiable convex optimization problems, in which each local cost function is composed of a twice differentiable convex function and a lower semi-continuous convex function. Motivated by the proximal operator and derivative feedback methods, continuous distributed optimization algorithms for both single-integrator and double-integrator multi-agent systems are developed to achieve distributed optimal consensus. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.