A Distributed Network System for Nonsmooth Coupled-Constrained Optimization

This paper addresses a class of distributed nonsmooth optimization problems whose objective function is a sum of convex local objective functions subjected to local set constraints and heterogeneous coupled constraints, including inequality and equality ones. To settle the problem, based on the consensus protocol for the Lagrangian multipliers of coupled constraints, we propose a distributed multi-agent network system with projected output feedback, which is different from the common projected primal-dual subgradient flow. It is proved that the output vector of the system is convergent to the optimal solution of the optimization problem from any initial state over connected communication networks. Finally, the effectiveness of the system is illustrated via two numerical examples.