Multistage stochastic convex programs: Duality and its implications |
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Authors: | Julia L Higle Suvrajeet Sen |
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Institution: | (1) SIE Dept. University of Arizona, Tucson, AZ, 85721 |
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Abstract: | In this paper, we study alternative primal and dual formulations of multistage stochastic convex programs (SP). The alternative
dual problems which can be traced to the alternative primal representations, lead to stochastic analogs of standard deterministic
constructs such as conjugate functions and Lagrangians. One of the by-products of this approach is that the development does
not depend on dynamic programming (DP) type recursive arguments, and is therefore applicable to problems in which the objective
function is non-separable (in the DP sense). Moreover, the treatment allows us to handle both continuous and discrete random
variables with equal ease. We also investigate properties of the expected value of perfect information (EVPI) within the context
of SP, and the connection between EVPI and nonanticipativity of optimal multipliers. Our study reveals that there exist optimal
multipliers that are nonanticipative if, and only if, the EVPI is zero. Finally, we provide interpretations of the retroactive
nature of the dual multipliers.
This work was supported by NSF grant DMII-9414680. |
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Keywords: | Stochastic Programming Duality EVPI |
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