Distributed Nonconvex Optimization via Bounded Gradient-Free Inputs

This article investigates the problem of distributed optimization over multiagent networks with the global objective being the sum of a set of possibly nonconvex functions. Based on recent developments in distributed average tracking as well as distributed extremum seeking, a distributed bounded gradient-free optimization algorithm is proposed. It is shown that the proposed scheme is able to solve nonconvex optimization problems with arbitrary prescribed accuracy. The relationship between the optimization error and control parameters is established with the error bound's explicit dependence on the bounds of agents' control inputs, which clearly demonstrates a tradeoff between the optimization error and input bound. An illustrative example is included to validate the effectiveness of proposed scheme.