Distributed Event-Triggered Projection Subgradient Algorithm over Unbalanced Digraphs Based on Row-Stochastic Matrices

Abstract

In this paper, we address the convex optimization problem on the multi-agent network, where the objective function is the summation of individual objectives of all agents. The communication graph among the agents is assumed to be directed and unbalanced with row-stochastic adjacency matrix. We devise a distributed projection sub-gradient algorithm with event-triggered communications, which is proved to asymptotically solve the convex optimization problem under diminishing stepsizes and mild triggering conditions. Finally, a numerical experiment is illustrated to demonstrate the reasonableness and validity of the theoretical analysis.