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Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs

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  • Raymond K.-M. Cheung

    (Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong)

  • Warren B. Powell

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544)

Abstract

We consider the problem of approximating the expected recourse function for two-stage stochastic programs. Our problem is motivated by applications that have special structure, such as an underlying network that allows reasonable approximations to the expected recourse function to be developed. In this paper, we show how these approximations can be improved by combining them with sample gradient information from the true recourse function. For the case of strictly convex nonlinear approximations, we prove convergence for this hybrid approximation. The method is attractive for practical reasons because it retains the structure of the approximation.

Suggested Citation

  • Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:1:p:73-79
    DOI: 10.1287/opre.48.1.73.12452
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
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    3. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    4. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    5. Andrzej Ruszczyński, 1987. "A Linearization Method for Nonsmooth Stochastic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 12(1), pages 32-49, February.
    6. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
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    Citations

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    Cited by:

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    3. Fan, Wei & Machemehl, Randy, 2004. "A Multi-stage Monte Carlo Sampling Based Stochastic Programming Model for the Dynamic Vehicle Allocation Problem," 45th Annual Transportation Research Forum, Evanston, Illinois, March 21-23, 2004 208244, Transportation Research Forum.
    4. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    5. ZhenFang Liu & GuoHe Huang, 2009. "Dual-Interval Two-Stage Optimization for Flood Management and Risk Analyses," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(11), pages 2141-2162, September.
    6. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    7. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    8. Song, Haiqing & Huang, Huei-Chuen, 2008. "A successive convex approximation method for multistage workforce capacity planning problem with turnover," European Journal of Operational Research, Elsevier, vol. 188(1), pages 29-48, July.

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