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Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

Author

Listed:
  • Niels Laan

    (University of Groningen)

  • Ward Romeijnders

    (University of Groningen)

  • Maarten H. Vlerk

    (University of Groningen)

Abstract

We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3–46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables.

Suggested Citation

  • Niels Laan & Ward Romeijnders & Maarten H. Vlerk, 2018. "Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations," Computational Management Science, Springer, vol. 15(3), pages 325-349, October.
    • Handle: RePEc:spr:comgts:v:15:y:2018:i:3:d:10.1007_s10287-018-0315-z
    DOI: 10.1007/s10287-018-0315-z
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    References listed on IDEAS

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    1. Ward Romeijnders & David P. Morton & Maarten H. van der Vlerk, 2017. "Assessing the Quality of Convex Approximations for Two-Stage Totally Unimodular Integer Recourse Models," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 211-231, May.
    2. Lewis Ntaimo, 2013. "Fenchel decomposition for stochastic mixed-integer programming," Journal of Global Optimization, Springer, vol. 55(1), pages 141-163, January.
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    Cited by:

    1. Ward Romeijnders & Niels van der Laan, 2020. "Pseudo-Valid Cutting Planes for Two-Stage Mixed-Integer Stochastic Programs with Right-Hand-Side Uncertainty," Operations Research, INFORMS, vol. 68(4), pages 1199-1217, July.

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