Exact convergence of gradient-free distributed optimization method in a multi-agent system

Abstract

© 2018 IEEE. In this paper, a gradient-free algorithm is proposed for a set constrained distributed optimization problem in a multi-agent system under a directed communication network. For each agent, a pseudo-gradient is designed locally and utilized instead of the true gradient information to guide the decision variables update. Compared with most gradient-free optimization methods where a doubly-stochastic weighting matrix is usually employed, this algorithm uses a row-stochastic matrix plus a column-stochastic matrix, and is able to achieve exact asymptotic convergence to the optimal solution.