Polyhedral convex feasible regions in stochastic programming with recourse

Abstract

Multistage stochastic programming with recourse is formulated in terms of a recursive sequence of mathematical programming problems--P0,..., PK--with stochastic data. A polyhedral property of their feasible regions is used to derive a Lipschitz property of their objective functions. A slightly stronger property is used to conclude that any measurable decision rule satisfying the explicit and Implicit constraints of Pk(0 ¿ k ¿ K) almost surely can be redefined on a set of measure 0 so it satisfies the constraints for every possible realization of the random variables. Sufficient conditions for each of the two polyhedral convexity properties are given.