Asymptotic Behavior of Optimal Solutions in Stochastic Programming

Asymptotic behavior of optimal solutions x̂_n of a sequence of stochastic programming problems is studied. Variational and generalized equations approaches are discussed. An expansion of x̂_n in terms of a parametrized mathematical programming problem, depending on a single random vector, is given. When optimal solutions of the parametrized program are directionally differentiable, this expansion leads to a close form expression for the asymptotic distribution of x̂_n. Applicability of the involved regularity conditions to nondifferentiable cases, and in particular to stochastic programming with recourse, is discussed.