A two-stage stochastic
programming problem with recourse is studied here in terms of an extended
Lagrangian function which allows certain multipliers to be elements of a dual space
(ℒ∞)∗, rather than an ℒ1 space. Such multipliers can be decomposed into an
ℒ1-component and a “singular” component. The generalization makes it possible to
characterize solutions to the problem in terms of a saddle-point, if the problem is
strictly feasible. The Kuhn-Tucker conditions for the basic duality framework
are modified to admit singular multipliers. It is shown that the optimal
multiplier vectors in the extended dual problem are, in at least one broad case,
ideal limits of maximizing sequences of multiplier vectors in the basic dual
problem.
