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Constraint generation for risk averse two-stage stochastic programs

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  • Mínguez, R.
  • van Ackooij, W.
  • García-Bertrand, R.

Abstract

A significant share of stochastic optimization problems in practice can be cast as two-stage stochastic programs. If uncertainty is available through a finite set of scenarios, which frequently occurs, and we are interested in accounting for risk aversion, the expectation in the recourse cost can be replaced with a worst-case function (i.e., robust optimization) or another risk-functional, such as conditional value-at-risk. In this paper we are interested in the latter situation especially when the number of scenarios is large. For computational efficiency we suggest a (clustering and) constraint generation algorithm. We establish convergence of these two algorithms and demonstrate their effectiveness through various numerical experiments.

Suggested Citation

  • Mínguez, R. & van Ackooij, W. & García-Bertrand, R., 2021. "Constraint generation for risk averse two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 288(1), pages 194-206.
    • Handle: RePEc:eee:ejores:v:288:y:2021:i:1:p:194-206
    DOI: 10.1016/j.ejor.2020.05.064
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    References listed on IDEAS

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    1. Alexandra Künzi-Bay & János Mayer, 2006. "Computational aspects of minimizing conditional value-at-risk," Computational Management Science, Springer, vol. 3(1), pages 3-27, January.
    2. S. E. Wright, 1994. "Primal-Dual Aggregation and Disaggregation for Stochastic Linear Programs," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 893-908, November.
    3. W. Ackooij & I. Danti Lopez & A. Frangioni & F. Lacalandra & M. Tahanan, 2018. "Large-scale unit commitment under uncertainty: an updated literature survey," Annals of Operations Research, Springer, vol. 271(1), pages 11-85, December.
    4. Wolf, Christian & Fábián, Csaba I. & Koberstein, Achim & Suhl, Leena, 2014. "Applying oracles of on-demand accuracy in two-stage stochastic programming – A computational study," European Journal of Operational Research, Elsevier, vol. 239(2), pages 437-448.
    5. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    6. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    7. Wim van Ackooij & Welington de Oliveira & Yongjia Song, 2018. "Adaptive Partition-Based Level Decomposition Methods for Solving Two-Stage Stochastic Programs with Fixed Recourse," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 57-70, February.
    8. René Henrion & Christian Küchler & Werner Römisch, 2009. "Scenario reduction in stochastic programming with respect to discrepancy distances," Computational Optimization and Applications, Springer, vol. 43(1), pages 67-93, May.
    9. Lemaréchal, C. & Nemirovskii, A. & Nesterov, Y., 1995. "New variants of bundle methods," LIDAM Reprints CORE 1166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    12. Holger Heitsch & Werner Römisch, 2009. "Scenario tree reduction for multistage stochastic programs," Computational Management Science, Springer, vol. 6(2), pages 117-133, May.
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