Continuous-Time Algorithm for Distributed Nonsmooth Optimization via Decomposition Design

This paper is concerned with a class of distributed nonsmooth convex constrained optimization problems with set constraints. The objective function is a sum of local convex functions, which are not necessarily differentiable. A new distributed continuous-time gradient-based algorithm using the decomposition design is explicitly constructed to solve the distributed optimization problem. Rigorous proofs using nonsmooth convex optimization theory and stability theory of differential inclusions are presented. A numerical simulation is conducted to show the efficacy of the proposed algorithm.