Strong Duality Theory For Distributed Stochastic Optimization Problems Based On Wasserstein Distance

The Divided Brute Stochastic Optimization(DRSO)problem is a theory developed based on the field of convex analysis stochastic optimization.In or-der to eliminate the interference of the random perturbation in the solution of the optimal solution in the DRSO problem,this paper discusses the distributed stochastic optimization problem based on Wasserstein distance,and proves that the strong duality theorem of this problem is valid in two special cases.The one case of it is that Wasserstein distance metric d(ζ,·)is a quasi-convex function onζ,and the objective function f(x,ζ)is an upper-bounded quasi-quasi Concave function.;another one is that Wasserstein distance metric d(ζ,·)is a convex func-tion aboutζ,and the objective function f(x,ζ)is a sliced concave function ofζ.Finally,the conclusions are verified using comparative numerical experiment ideas,and ideas and suggestions are proposed for subsequent research.