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Parallelizable Preprocessing Method for Multistage Stochastic Programming Problems

Author

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  • X. W. Liu

    (Hebei University of Technology)

  • M. Fukushima

    (Kyoto University)

Abstract

Stochastic programming has extensive applications in practical problems such as production planning and portfolio selection. Typically, the model has very large size and some techniques are often used to exploit the special structure of the programs. It has been noticed that the coefficient matrix may not be of full rank in the well-known scenario formulation of stochastic programming; thus, the preprocessing is often necessary in developing rapid decomposition methods. In this paper, we propose a parallelizable preprocessing method, which exploits effectively the structure of the formulation. Although the underlying idea is simple, the method turns out to be very useful in practice, since it may help us to select the nonanticipativity constraints efficiently. Some numerical results are reported confirming the usefulness of the method.

Suggested Citation

  • X. W. Liu & M. Fukushima, 2006. "Parallelizable Preprocessing Method for Multistage Stochastic Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 327-346, December.
    • Handle: RePEc:spr:joptap:v:131:y:2006:i:3:d:10.1007_s10957-006-9156-y
    DOI: 10.1007/s10957-006-9156-y
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    References listed on IDEAS

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    1. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
    2. Zhang, S., 2002. "An interior-point and decomposition approach to multiple stage stochastic programming," Econometric Institute Research Papers EI 2002-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    4. John R. Birge & Liqun Qi, 1988. "Computing Block-Angular Karmarkar Projections with Applications to Stochastic Programming," Management Science, INFORMS, vol. 34(12), pages 1472-1479, December.
    5. Arjan Berkelaar & Cees Dert & Bart Oldenkamp & Shuzhong Zhang, 2002. "A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming," Operations Research, INFORMS, vol. 50(5), pages 904-915, October.
    6. Irvin J. Lustig & John M. Mulvey & Tamra J. Carpenter, 1991. "Formulating Two-Stage Stochastic Programs for Interior Point Methods," Operations Research, INFORMS, vol. 39(5), pages 757-770, October.
    7. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
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