Distributed Event-Triggered Algorithm for Convex Optimization with Coupled Constraints

TL;DR

This paper introduces a distributed primal-dual algorithm with event-triggered communication for convex optimization problems with coupled constraints, achieving exact convergence with reduced communication costs.

Contribution

It presents a novel distributed primal-dual algorithm using constant step-sizes and event-triggered communication, ensuring exact convergence and reduced communication overhead.

Findings

Achieves $O(1/k)$ convergence rate for convex objectives.

Reduces communication cost via event-triggered mechanism.

Verifies effectiveness through numerical example.

Abstract

This paper develops a distributed primal-dual algorithm via 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 $O(1/k)$ convergence rate for general convex objective functions, where $k>0$ is the iteration number. Moreover, by applying 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.