Stochastic Convex Programming: Relatively Complete Recourse and Induced Feasibility
R. TYRRELL ROCKAFELLAR, Roger J.‐B. Wets · SIAM Journal on Control and Optimization · 1976
The basic dual problem and extended dual problem associated with a two-stage stochastic program are shown to be equivalent, if the program is strictly feasible and satisfies a condition generalizing, in a sense, the condition of relatively complete recourse in stochastic linear programming. Combined with earlier results, this yields the fact that, under the same assumptions, solutions to the program can be characterized in terms of saddle points of the basic Lagrangian. A couple of examples are used to illustrate the salient points of the theory. The last section contains a review of the principal implications of the results of this paper combined with those of three preceding papers also devoted to stochastic convex programs.