Gradient-free distributed optimization with exact convergence

In this paper, a gradient-free distributed algorithm is introduced to solve set constrained optimization problem under directed communication network . Specifically, at each time-step, the agents locally compute so-called pseudo-gradient guide updates of decision variables, which can be applied in fields where gradient information unknown, not available or non-existent. A surplus-based method adopted remove doubly stochastic requirement on weighting matrix, enables implementation graphs having no associated matrix. For convergence results, proposed able obtain exact optimal value with any positive, non-summable and non-increasing step-sizes. Furthermore, when step-size also square-summable, guaranteed achieve an solution. addition standard analysis, rate investigated. Finally, effectiveness verified through numerical simulations.