Distributed event-triggered algorithm for convex optimization with coupled constraints

Abstract

This paper develops a distributed primal–dual algorithm via an event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some existing distributed algorithms with the diminishing step-sizes, our algorithm uses the constant step-sizes, and is shown to achieve an exact convergence to an optimal solution with an ergodic convergence rate of $O(1/k)$ for general convex objective functions, where $k>0$ is the iteration number. Based on the event-triggered communication mechanism, the proposed algorithm can effectively reduce the communication cost without sacrificing the convergence rate. Finally, a numerical example is presented to verify the effectiveness of the proposed algorithm.