Analysis of stochastic dual dynamic programming method

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...

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Veröffentlicht in:European journal of operational research Jg. 209; H. 1; S. 63 - 72
1. Verfasser: Shapiro, Alexander
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 16.02.2011
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
Algorithms
Applied sciences
Complexity theory
Dynamic programming
Exact sciences and technology
Linear programming
Mathematical programming
Mathematics
Monte Carlo sampling
Operational research and scientific management
Operational research. Management science
Probability and statistics
Risk averse optimization
Risk aversion
Sample Average Approximation method
Sampling theory, sample surveys
Sciences and techniques of general use
Statistics
Stochastic Dual Dynamic Programming algorithm
Stochastic models
Stochastic programming
Stochastic programming Stochastic Dual Dynamic Programming algorithm Sample Average Approximation method Monte Carlo sampling Risk averse optimization
Studies
Monte Carlo sampling
Risk averse optimization
Stochastic Dual Dynamic Programming algorithm
Sample Average Approximation method
Stochastic programming
Stochastic convergence
Monte Carlo method
Multistage method
Statistical analysis
Linear programming
Stochastic method
Computational complexity
Dynamic method
Optimization
Risk aversion
Stochastic analysis
Approximation method
Stochastic Dual Dynamic Programming
Dynamic programming
algorithm
ISSN:0377-2217, 1872-6860
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Beschreibung
Zusammenfassung: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 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.
Bibliographie:SourceType-Scholarly Journals-1
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content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.08.007