Duality for Stochastic Programming Interpreted as L. P. in $L_p $-Space
Mark J. Eisner, Paul Olsen · SIAM Journal on Applied Mathematics · 1975
The linearly constrained multistage stochastic programming problem is interpreted as a programming problem in $L_p $-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 $\mathcal{C}$, 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 $\mathcal{C}$ follows from simple conditions on the technology matrix A for the problem.