Distributed Randomized Gradient-Free Optimization Protocol of Multiagent Systems Over Weight-Unbalanced Digraphs

In this paper, a distributed randomized gradient-free optimization protocol of multiagent systems over weight-unbalanced digraphs described by row-stochastic matrices is proposed to solve a distributed constrained convex optimization problem. Each agent possesses its local nonsmooth, but Lipschitz continuous, objective function and assigns the weight to information gathered from in-neighbor agents to update its decision state estimation, which is applicable and straightforward to implement. In addition, our algorithm relaxes the requirements of diminishing step sizes to only a nonsummable condition under convex bounded constraint sets. The boundedness and ultimate limit, instead of the supermartingale convergence theorem, are utilized to analyze the consistency and convergence and demonstrate convergence rates with different step sizes. Finally, the validity of the proposed algorithm is verified through numerical examples.