ASYMPTOTIC-BEHAVIOR OF OPTIMAL-SOLUTIONS IN STOCHASTIC-PROGRAMMING

Asymptotic behavior of optimal solutions x(n) of a sequence of stochastic programming Problems is studied. Variational and generalized equations approaches are discussed. An expansion of x(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 x(n). Applicability of the involved regularity conditions to nondifferentiable cases, and in particular to stochastic programming with recourse, is discussed.