In many optimization problems arising from scientific, engineering and artificial intelligence
applications, objective and constraint functions are available only as the output of a black …

We propose an approach based on function evaluations and Bayesian inference to extract
higher-order differential information of objective functions from a given ensemble of …

Abstract Using the Moore–Penrose pseudoinverse this work generalizes the gradient
approximation technique called the centred simplex gradient to allow sample sets …

This work presents a novel matrix-based method for constructing an approximation Hessian
using only function evaluations. The method requires less computational power than …

Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms
that do not use derivatives. One branch of DFO focuses on model-based DFO methods …

Variational Analysis studies mathematical objects under small variations. With regards to
optimization, these objects are typified by representations of first-order or second-order …

This work investigates finite differences and the use of (diagonal) quadratic interpolation
models to obtain approximations to the first and (non-mixed) second derivatives of a …

Minimising a nonlinear function is a ubiquitous problem in applications, and standard
algorithms need accurate evaluations of the function and its derivatives. However, if the …

The simplex gradient, a popular numerical differentiation method due to its flexibility, lacks a
principled method by which to construct the sample set, specifically the location of function …

This manuscript derives locally weighted ensemble Kalman methods from the point of view
of ensemble-based function approximation. This is done by using pointwise evaluations to …