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, σ R"*) so as to satisfy the constraints and minimize total expected cost, where σ 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. 12., Characterization of the subdifferentials of convex functions, Pacific J. Math., 17 (1966),

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