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

A Gradient-Free Distributed Optimization Method for Convex Sum of Non-Convex Cost Functions