A duality theory is developed
for stochastic programs with convex objective and convex constraints. The problem
consists in selecting x1∈ Rn1 and x2∈ℒ∞(S,Σ,σ;Rn2) 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 x1 and x2(s)
belong to compact subsets of Rn1 and Rn2 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.
