A Gradient-free Penalty ADMM for Solving Distributed Convex Optimization Problems with Feasible Set Constraints

In this paper, we propose a gradient-free penalty ADMM to distributedly solve constrained convex optimization problems over network systems. All agents only communicate with their neighbors and local decision variables constrained in feasible set constraints. We design a pseudo-gradient to obtain an approximate gradient. Then we update decision variables based on the approximate gradient and penalty ADMM method. Moreover, we analyze the convergent performance of the proposed algorithm and summarize some conclusions.