A gradient‐free distributed optimization method for convex sum of nonconvex cost functions

This paper presents a special type of distributed optimization problems, where the summation agents' local cost functions (i.e., global function) is convex, but each individual can be non-convex. Unlike most algorithms by taking advantages gradient, considered problem allowed to non-smooth, and gradient information unknown agents. To solve problem, Gaussian-smoothing technique introduced gradient-free method proposed. We prove that agent's iterate approximately converges optimal solution both with probability 1 in mean, provide an upper bound on optimality gap, characterized difference between functional value value. The performance proposed algorithm demonstrated numerical example application privacy enhancement.