A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems

This paper discusses a generalized semi-infinite programming problem under uncertainty. The expected value approach is applied to define a deterministic version of the problem. We propose a new reformulation by using the first order optimality conditions of the second stage optimization problem. We then present a smoothing implicit programming method to solve the problem with finite discrete distribution. Global convergence results are obtained under mild conditions.