Abstract
A model of multistage stochastic programming over a scenario tree is developed, in whichthe evolution of information states, as represented by the nodes of a scenario tree, is supplementedby a dynamical system of state vectors controlled by recourse decisions. A dualproblem is obtained in which multipliers associated with the primal dynamics are pricevectors that are propagated backward in time through a dual dynamical system involvingconditional expectation. A format of Fenchel duality is employed in order to have immediatespecialization not only to linear programming but also to extended linear‐quadratic programming.The resulting optimality conditions support schemes of decomposition in which aseparate optimization problem is solved at each node of the scenario tree.
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Rockafellar, R. Duality and optimality in multistagestochastic programming. Annals of Operations Research 85, 1–19 (1999). https://doi.org/10.1023/A:1018909508556
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DOI: https://doi.org/10.1023/A:1018909508556