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Global Stochastic Optimization with Low-Dispersion Point Sets

Author

Listed:
  • Sidney Yakowitz

    (Formerly Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona)

  • Pierre L'Ecuyer

    (Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal, H3C 3J7, Canada)

  • Felisa Vázquez-Abad

    (Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal, H3C 3J7, Canada)

Abstract

This study concerns a generic model-free stochastic optimization problem requiring the minimization of a risk function defined on a given bounded domain in a Euclidean space. Smoothness assumptions regarding the risk function are hypothesized, and members of the underlying space of probabilities are presumed subject to a large deviation principle; however, the risk function may well be nonconvex and multimodal. A general approach to finding the risk minimizer on the basis of decision/observation pairs is proposed. It consists of repeatedly observing pairs over a collection of design points. Principles are derived for choosing the number of these design points on the basis of an observation budget, and for allocating the observations between these points in both prescheduled and adaptive settings. On the basis of these principles, large-deviation type bounds of the minimizer in terms of sample size are established.

Suggested Citation

  • Sidney Yakowitz & Pierre L'Ecuyer & Felisa Vázquez-Abad, 2000. "Global Stochastic Optimization with Low-Dispersion Point Sets," Operations Research, INFORMS, vol. 48(6), pages 939-950, December.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:6:p:939-950
    DOI: 10.1287/opre.48.6.939.12393
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    References listed on IDEAS

    as
    1. Pierre L'Ecuyer & Gaétan Perron, 1994. "On the Convergence Rates of IPA and FDC Derivative Estimators," Operations Research, INFORMS, vol. 42(4), pages 643-656, August.
    2. Frank J. Matejcik & Barry L. Nelson, 1995. "Two-Stage Multiple Comparisons with the Best for Computer Simulation," Operations Research, INFORMS, vol. 43(4), pages 633-640, August.
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    Cited by:

    1. Sigurdur Ólafsson, 2004. "Two-Stage Nested Partitions Method for Stochastic Optimization," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 5-27, March.
    2. Justin Boesel & Barry L. Nelson & Seong-Hee Kim, 2003. "Using Ranking and Selection to “Clean Up” after Simulation Optimization," Operations Research, INFORMS, vol. 51(5), pages 814-825, October.
    3. Arsham Hossein, 2007. "Monte Carlo Techniques for Parametric Finite Multidimensional Integral Equations," Monte Carlo Methods and Applications, De Gruyter, vol. 13(3), pages 173-195, August.
    4. Ullrich, Mario, 2018. "A lower bound for the dispersion on the torus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 186-190.

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