An exact penalty method for constrained distributed optimization

This paper focuses on a distributed non-smooth constrained optimization problem, in which the non-smoothness means the continuity but non-differentiability. Distributed optimization deals with optimizing a sum of objective functions, each function is known by one agent due to many reasons such as privacy and security. And all the agent reach an global optimal by communicating through an interaction graph. We proposed an exact penalty algorithm for constrained distributed optimization, which has some good properties when we design a continuous-time algorithm. Then we rigorously prove the efficiency of this method. We also put a numerical example to show the efficacy of the proposed algorithm.