Lipschitz constants in experimental optimization

TL;DR

This paper explores how Lipschitz constants can be explicitly used in experimental optimization to ensure constraint satisfaction and mitigate uncertainty effects, providing new methods and refinements.

Contribution

It introduces novel approaches for applying Lipschitz constants in engineering-based experimental optimization and discusses techniques for setting these constants.

Findings

Lipschitz constants can help ensure constraint satisfaction.

They can reduce negative effects of measurement uncertainty.

Refinements improve the practical application of these methods.

Abstract

The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically oriented applications, but their potential for explicit use in more engineering-based domains has not been explored. The latter point is the subject of this paper, where we propose several ways in which the Lipschitz constants may be used explicitly in the domain of experimental optimization. Specifically, we focus on how they may help ensure the satisfaction of constraints and on their potential role in reducing the negative effects of measurement or estimation uncertainty. A number of refinements to the proposed approaches are also derived, and some techniques for setting the constants are presented.