Abstract
A new duality theory is developed for a class of two-stage stochastic programs in which the probability distribution is not necessarily discrete, providing a new framework for problems which do not necessarily have relatively complete recourse and do not satisfy the typical Slater conditions. The results instead rely on the much weaker constraint qualification of ‘calmness’ of certain finite-dimensional marginal functions to derive the existence of finite-dimensional Lagrange multipliers. In this way, strong duality results are established in which the dual problems are finite-dimensional, despite the possible infinite-dimensional character of the second-stage constraints. Numerical possibilities for this class of problems are highlighted.
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Korf, L.A. (2001). A Finite-Dimensional Approach to Infinite-Dimensional Constraints in Stochastic Programming Duality. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications. Applied Optimization, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6594-6_8
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DOI: https://doi.org/10.1007/978-1-4757-6594-6_8
Publisher Name: Springer, Boston, MA
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