We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and un...
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We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of stochasticdualdynamicprogramming, cutting-plane and partial-sampling (CUPPS) algorithm, and dynamic outer-approximation sampling algorithms when applied to problems with general convex cost functions.
In this paper we discuss statistical properties and convergence of the stochasticdualdynamicprogramming (SDDP) method applied to multistage linear stochasticprogramming problems. We assume that the underline data ...
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In this paper we discuss statistical properties and convergence of the stochasticdualdynamicprogramming (SDDP) method applied to multistage linear stochasticprogramming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently the SDDP algorithm is applied to the constructed Sample Average Approximation (SAA) problem. Then we proceed to analysis of the SDDP solutions of the SAA problem and their relations to solutions of the "true" problem. Finally we discuss an extension of the SDDP method to a risk averse formulation of multistage stochastic programs. We argue that the computational complexity of the corresponding SDDP algorithm is almost the same as in the risk neutral case. (C) 2010 Elsevier B.V. All rights reserved.
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