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Sample average approximation of expected value constrained stochastic programs

Authors:

Shabbir AhmedAuthors Info & Claims

Operations Research Letters, Volume 36, Issue 5

Pages 515 - 519

https://doi.org/10.1016/j.orl.2008.05.003

Published: 01 September 2008 Publication History

Abstract

We propose a sample average approximation (SAA) method for stochastic programming problems with expected value constraints. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). We provide a convergence analysis and a statistical validation scheme for the proposed method.

References

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S. Ahmed, A. Shapiro, The sample average approximation method for stochastic programs with integer recourse, Technical Report, Georgia Institute of Technology, 2002. Available at: www.optimization-online.org

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Atlason, J., Epelman, M. and Henderson, G., Call center staffing with simulation and cutting plane methods. Annals of Operations Research. v127. 333-358.

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Fábián, C.I., Handling CVaR objectives and constraints in two-stage stochastic models. European Journal of Operational Research. v191. 888-911.

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Fabian, C.I. and Veszpremi, A., Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance. Journal of Risk. v10. 111-131.

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Klein Haneveld, W., Duality in stochastic linear and dynamic programming. In: Lecture Notes in Economics and Math. Systems, vol. 274. Springer, Berlin.

Digital Library

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Higle, J.L. and Sen, S., Statistical approximations for recourse constrained stochastic programs. Annals of Operations Research. v56. 157-175.

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Kleywegt, A.J., Shapiro, A. and Homem-De-Mello, T., The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization. v12. 479-502.

Digital Library

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Krokhmal, P., Palmquist, J. and Uryasev, S., Portfolio optimization with conditional value-at-risk objective and constraints. The Journal of Risk. v4. 11-27.

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D. Kuhn, Convergent bounds for stochastic programs with expected value constraints, Stochastic Programming E-Print Series, www.speps.org, 2006

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Rockafellar, R.T. and Uryasev, S., Optimization of conditional value-at-risk. The Journal of Risk. v2. 21-41.

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. 2003. Stochastic programming, Handbooks in OR & MS, 2003.Elsevier Science, Amsterdam.

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Stroock, D.W., An Introduction to the theory of large deviations. 1984. Springer-Verlag, New York.

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W. Wang, Sample average approximation of risk-averse stochastic programs, Ph.D. Thesis, Georgia Institute of Technology, 2007

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W. Wang, S. Ahmed, Sample average approximation of expected value constrained stochastic programs, Technical Report, Georgia Institute of Technology, 2007. Available at: www.optimization-online.org

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W. Wang, S. Ahmed, Online supplement to Sample average approximation of expected value constrained stochastic programs, 2008. Available at: www.isye.gatech.edu/~sahmed/evcsupplement.pdf

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Sample average approximation of expected value constrained stochastic programs
1. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image Operations Research Letters

Operations Research Letters Volume 36, Issue 5

September, 2008

143 pages

ISSN:0167-6377

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Copyright © Elsevier B.V. © 2008.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 September 2008

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Löhndorf NWozabal D(2023)The Value of Coordination in Multimarket Bidding of Grid Energy StorageOperations Research10.1287/opre.2021.224771:1(1-22)Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1287/opre.2021.2247
Chamon LPaternain SCalvo-Fullana MRibeiro A(2023)Constrained Learning With Non-Convex LossesIEEE Transactions on Information Theory10.1109/TIT.2022.318794869:3(1739-1760)Online publication date: 1-Mar-2023
https://dl.acm.org/doi/10.1109/TIT.2022.3187948
Xue SSun YYurochkin MKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Calibrated data-dependent constraints with exact satisfaction guaranteesProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600890(8526-8537)Online publication date: 28-Nov-2022
https://dl.acm.org/doi/10.5555/3600270.3600890
Sur ABirge J(2022)Asymptotic behavior of solutions: An application to stochastic NLPMathematical Programming: Series A and B10.1007/s10107-020-01554-6191:1(281-306)Online publication date: 1-Jan-2022
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Krklec Jerinkić NRožnjik A(2020)Penalty variable sample size method for solving optimization problems with equality constraints in a form of mathematical expectationNumerical Algorithms10.1007/s11075-019-00699-683:2(701-718)Online publication date: 1-Feb-2020
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Ta TMai TBastin FL’Ecuyer P(2020)On a multistage discrete stochastic optimization problem with stochastic constraints and nested samplingMathematical Programming: Series A and B10.1007/s10107-020-01518-w190:1-2(1-37)Online publication date: 12-Jun-2020
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