Response surface methodology: Asymptotic normality of the optimal solution

TL;DR

This paper analyzes the sensitivity and asymptotic behavior of the optimal solution in response surface methodology, providing explicit effects of perturbations and characterizing critical points in convex optimization.

Contribution

It offers a detailed sensitivity analysis and proves the asymptotic normality of the optimal solution in response surface models, including explicit perturbation effects.

Findings

Explicit form of perturbation effects on the optimal solution

Characterization of critical points in convex response surface models

Asymptotic normality of the optimal solution

Abstract

Sensitivity analysis of the optimal solution in response surface methodology is studied and an explicit form of the effect of perturbation of the regression coefficients on the optimal solution is obtained. The characterisation of the critical point of the convex program corresponding to the optimum of a response surface model is also studied. The asymptotic normality of the optimal solution follows by standard methods.