# Gabriel Jarry-BolducUBC · Department of Mathematics

Gabriel Jarry-Bolduc

PhD Candidate in mathematics at UBC

## About

16

Publications

1,112

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28

Citations

Introduction

**Skills and Expertise**

Education

September 2017 - May 2022

September 2016 - May 2017

September 2014 - April 2016

## Publications

Publications (16)

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 technique called generalized centered simplex gradient is used to approximate the gradient, then the formula can be computed for only one additional function evaluation. An erro...

The properties of positive bases make them a useful tool in derivative-free optimization (DFO) and an interesting concept in mathematics. The notion of the \emph{cosine measure} helps to quantify the quality of a positive basis. It provides information on how well the vectors in the positive basis uniformly cover the space considered. The number of...

Model-based methods are popular in derivative-free optimization (DFO). In most of them, a single model function is built to approximate the objective function. This is generally based on the assumption that the objective function is one blackbox. However, some real-life and theoretical problems show that the objective function may consist of severa...

An explicit formula to approximate the diagonal entries of the Hessian is introduced. When the derivative-free technique called \emph{generalized centered simplex gradient} is used to approximate the gradient, then the formula can be computed for only one additional function evaluation. An error bound is introduced and provides information on the f...

This work investigates the asymptotic behaviour of the gradient approximation method called the generalized simplex gradient (GSG). This method has an error bound that at first glance seems to tend to infinity as the number of sample points increases, but with some careful construction, we show that this is not the case. For functions in finite dim...

Using the Moore–Penrose pseudoinverse this work generalizes the gradient approximation technique called the centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the generalized centred simplex gradient. We develop error bounds and, under a full-rank condition, show that the error boun...

This work introduces the nested-set Hessian approximation, a second-order approximation method that can be used in any derivative-free optimization routine that requires such information. It is built on the foundation of the generalized simplex gradient and proved to have an error bound that is on the order of the maximal radius of the two sets use...

We consider the question of numerically approximating the derivative of a smooth function using only function evaluations. In particular, we examine the regression gradient, the generalized simplex gradient and the generalized centered simplex gradient, three numerical techniques based on using function values at a collection of sample points to co...

A simplex, the convex hull of a set of \(n+1\) affinely independent points, is a useful tool in derivative-free optimization. The term uniform simplex was used by Audet and Hare (Derivative-free and blackbox optimization. Springer series in operations research and financial engineering, Springer, Cham, 2017). The purpose of this paper is to provide...

Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the cosine measure and convergence properties of certain DFO algorithms are intimately linked to the value of this me...

Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the \emph{generalized centred simplex gradient}. We develop error bounds and, under a full-rank condition, show that the error...

Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the {\em cosine measure} and convergence properties of certain DFO algorithms are intimately linked to the value of t...

Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the cosine measure and convergence properties of certain DFO algorithms are intimately linked to the value of this me...

We consider the question of numerically approximating the derivative of a smooth function using only function evaluations. In particular, we examine the regression gradient, the generalized simplex gradient and the generalized centered simplex gradient, three numerical techniques based on using function values at a collection of sample points to co...

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 [14]. Unfortunately, those calculus rules only work under a restrictive set of assumptions. The purpose of this paper...