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Duality and optimality in multistage stochastic programming
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DOI：10.1023/A:1018909508556.png)
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Abstract
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A model of multistage stochastic programming over a scenario tree is developed, in which the evolution of information states, as represented by the nodes of a scenario tree, is supplemented by a dynamical system of state vectors controlled by recourse decisions. A dual problem is obtained in which multipliers associated with the primal dynamics are price vectors that are propagated backward in time through a dual dynamical system involving conditional expectation. A format of Fenchel duality is employed in order to have immediate specialization not only to linear programming but also to extended linear-quadratic programming. The resulting optimality conditions support schemes of decomposition in which a separate optimization problem is solved at each node of the scenario tree.
Keywords:
LINEAR-QUADRATIC PROBLEMS
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