On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize...

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Bibliographic Details
Published in:Computational optimization and applications 2019-09, Vol.74 (1), p.1-42
Main Authors: van Ackooij, Wim, de Oliveira, Welington, Song, Yongjia
Format: Article
Language:English
Subjects:
Algorithms
Convex and Discrete Geometry
Decomposition
Dynamic programming
Management Science
Mathematical programming
Mathematics
Mathematics and Statistics
Multistage
Numerical methods
Operations Research
Operations Research/Decision Theory
Optimization
Optimization and Control
Production scheduling
Regularization
Statistics
Stochastic programming
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Summary:We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling problem indicate that our algorithms are competitive with the state-of-the-art approaches such as multistage regularized decomposition , nested decomposition and stochastic dual dynamic programming .
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00104-x