In this paper we discuss statistical properties and convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data ...
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In this paper we discuss statistical properties and convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming 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 sampleaverageapproximation (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.
In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensi...
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In this paper we consider optimization problems where the objective function is given in a form of the expectation. A basic difficulty of solving such stochastic optimization problems is that the involved multidimensional integrals (expectations) cannot be computed with high accuracy. The aim of this paper is to compare two computational approaches based on Monte Carlo sampling techniques, namely, the stochastic approximation (SA) and the sampleaverageapproximation (SAA) methods. Both approaches, the SA and SAA methods, have a long history. Current opinion is that the SAA method can efficiently use a specific (say, linear) structure of the considered problem, while the SA approach is a crude subgradient method, which often performs poorly in practice. We intend to demonstrate that a properly modified SA approach can be competitive and even significantly outperform the SAA method for a certain class of convex stochastic problems. We extend the analysis to the case of convex-concave stochastic saddle point problems and present (in our opinion highly encouraging) results of numerical experiments.
To deal with optimal design problem of manufacturing/remanufacturing (M/R) logistics network under uncertain circumstance, a two-stage stochastic-fuzzy programming model is developed, which involves continuous distrib...
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ISBN:
(纸本)9781424439706
To deal with optimal design problem of manufacturing/remanufacturing (M/R) logistics network under uncertain circumstance, a two-stage stochastic-fuzzy programming model is developed, which involves continuous distribution stochastic parameters and fuzzy triangle or tolerance parameters. With the help of the model, the following items can be computed such as the optimal sites and numbers of M/R factory, integrated center, distribution center and collection center, the quantities of logistics flow in the network and the minimum fee in the planning horizon. Applying the fuzzy chance-constrained programming approach, the proposed model is transformed into a pure stochastic programming model. To solve this model, a hybrid genetic algorithm is presented, the sample average approximation method is introduced, the optimal objective value approaching technique is presented, and the optimal design steps are summarized. Besides, the application of the proposed model is showed with an example.
In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved wi...
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In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.
In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved wi...
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In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.
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