Duality for Stochastic Programming Interpreted as L. P. in Lₚ-Space

The linearly constrained multistage stochastic programming problem is interpreted as a programming problem in Lₚ-space, linear if the stochastic problem is linear, and a duality theory is developed from the general results of Rockafellar [16]. The duality is symmetric for linear problems, provided that the stochastic model is suitably generalized, and can be given an economic interpretation. If a certain set C, closely related to the epigraph of the perturbation function, is closed, then the stochastic programming problem attains its minimum, which equals the supremum of the dual problem. The closedness of C follows from simple conditions on the technology matrix A for the problem.