Open Collections

Abstract

Simplex gradients, essentially the gradient of a linear approximation, are a popular tool in derivative-free optimization (DFO). In 2015, a product rule, a quotient rule and a sum rule for simplex gradients were introduced by Regis. Unfortunately, those calculus rules only work under a restrictive set of assumptions. The purpose of this thesis is to provide new calculus rules that work in a wider setting. The rules place minimal assumptions on the functions involved and the interpolation sets. The rules further lead to an alternative approach to gradient approximation in situations where the rules could be applied. We analyze the new approach, provide error bounds, include some testing on numerical stability and accuracy.