Global Stochastic Optimization with Low-Dispersion Point Sets

Sidney Yakowitz, Pierre L'Ecuyer () and Felisa Vázquez-Abad ()
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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

Operations Research, 2000, vol. 48, issue 6, 939-950

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.

Keywords: Simulation: stochastic optimization; design of experiments; Programming: stochastic; adaptive (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (4)

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