Achieving the Social Optimum in a Nonconvex Cooperative Aggregative Game: A Distributed Stochastic Annealing Approach

This brief designs a distributed stochastic annealing algorithm for nonconvex cooperative aggregative games, whose players' cost functions not only depend on players' own decision variables but also rely on the sum of players' decision variables. To seek the social optimum of cooperative aggregative games, a distributed stochastic annealing algorithm is proposed, where the local cost functions are nonconvex and the communication topology between players is time-varying. The weak convergence to the social optimum of the algorithm is further analyzed. A numerical example is finally given to illustrate the effectiveness of the proposed algorithm.