The Network Interdiction Problem involves interrupting an adversary’s ability to maximize flow through a capacitated network by destroying portions of the network. A budget constraint limits the amount of the network that can be destroyed. In this paper, we study a stochastic version of the network interdiction problem in which the successful destruction of an … Read more
We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs. … Read more
In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate piecewise structure and directional differentiability of both — the lower level equilibrium solution and objective integrant. We show almost sure convergence of optimal values, optimal solutions … Read more
This paper develops a solution strategy for two-stage stochastic programs with integer recourse. The proposed methodology relies on approximating the underlying stochastic program via sampling, and solving the approximate problem via a specialized optimization algorithm. We show that the proposed scheme will produce an optimal solution to the true problem with probability approaching one exponentially … Read more