ASTRO-DF is a prominent trust-region method using adaptive sampling for stochastic
derivative-free optimization of nonconvex problems. Its salient feature is an easy-to …

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 …

We present an enhanced stochastic trust-region optimization with adaptive sampling
(ASTRO-DF) in which optimizing an iteratively constructed local model on estimates of …

An explicit formula based on matrix algebra to approximate the diagonal entries of a
Hessian matrix with any number of sample points is introduced. When the derivative-free …

This paper presents two methods for approximating a proper subset of the entries of a
Hessian using only function evaluations. These approximations are obtained using the …

In this paper, we explore the two-point zeroth-order gradient estimator and identify the
optimal distribution of random perturbations that minimizes the estimator's variance. We …