Statitical testing of optimality conditions in multiresponse simulation-based optimization

Bert Bettonvil, Enrique del Castillo and Jack P.C. Kleijnen

No 81, Discussion Paper from Tilburg University, Center for Economic Research

Abstract: This paper derives a novel procedure for testing the Karush-Kuhn-Tucker (KKT) first-order optimality conditions in models with multiple random responses. Such models arise in simulation-based optimization with multivariate outputs. This paper focuses on expensive simulations, which have small sample sizes. The paper estimates the gradients (in the KKT conditions) through low-order polynomials, fitted locally. These polynomials are estimated using Ordinary Least Squares (OLS), which also enables estimation of the variability of the estimated gradients. Using these OLS results, the paper applies the bootstrap (resampling) method to test the KKT conditions. Furthermore, it applies the classic Student t test to check whether the simulation outputs are feasible, and whether any constraints are binding. The paper applies the new procedure to both a synthetic example and an inventory simulation; the empirical results are encouraging.

JEL-codes: C0 C1 C9 C15 C44 C61 C9 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cmp and nep-ecm
Date: 2005

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Related works:
Journal Article: Statistical testing of optimality conditions in multiresponse simulation-based optimization (2009)
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:kubcen:200581

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