| 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. |