Stochastic convex programming: basic duality

Abstract

A duality theory is developed for stochastic programs with convex objective and convex constraints. The problem consists in selecting x t E R n * and x 2 E (S, S, R"*) so as to satisfy the constraints and minimize total expected cost, where is a probability measure and the constraints as well as the objective are functions of the random elements of the problem. Under the additional restriction that JCI and x 2 (s) belong to compact subsets of R n ' and R "* respectively, it is shown that the problem is equivalent to the more common dynamic formulation for stochastic programs with recourse, a basic duality theorem -of the type min = sup -is proved and qualitative results on the existence of dual solutions are derived.