3 citations · 3 across the 13 of their papers we have counts for
13 papers
A -step generalization of the Q-order of convergence
Gabriel Jarry-Bolduc
The notion of Q-order convergence is arguably the most important tool for describing the asymptotic behavior of a convergent sequence. Loosely speaking, it captures the``speed''of…
The cosine measure of a function at a point
Warren Hare, Gabriel Jarry-Bolduc, Chayne Planiden
The cosine measure of a set of vectors in measures how well the set covers all directions in . It identifies the direction furthest, in angle, from the…
An algorithm to exactly compute minimal upper bounds in the Loewner order
Adam Humeniuk, Gabriel Jarry-Bolduc, Patrick Pascua +1
The Loewner order on Hermitian matrices is a partial order that compares matrices in terms of positive semidefiniteness. The Loewner order plays a key role in many fields such as o…
The cosine measure relative to a subspace
Charles Audet, Warren Hare, Gabriel Jarry-Bolduc
The cosine measure was introduced in 2003 to quantify the richness of a finite positive spanning sets of directions in the context of derivative-free directional methods. A positiv…
Using generalized simplex methods to approximate derivatives
Gabriel Jarry-Bolduc, Chayne Planiden
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 technique…
Using orthogonally structured positive bases for constructing positive -spanning sets with cosine measure guarantees
Warren Hare, Gabriel Jarry-Bolduc, Sébastien Kerleau +1
Positive spanning sets span a given vector space by nonnegative linear combinations of their elements. These have attracted significant attention in recent years, owing to their ex…
Error Analysis of Surrogate Models Constructed through Operations on Sub-models
Yiwen Chen, Gabriel Jarry-Bolduc, Warren Hare
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 ba…
Nicely structured positive bases with maximal cosine measure
Warren Hare, Gabriel Jarry-Bolduc, Chayne Planiden
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} he…
Approximating the diagonal of a Hessian: which sample set of points should be used
Gabriel Jarry-Bolduc
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…
Limiting behaviour of the generalized simplex gradient as the number of points tends to infinity on a fixed shape in R^n
Warren Hare, Gabriel Jarry-Bolduc, Chayne Planiden
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 gla…
Hessian approximations
Warren Hare, Gabriel Jarry-Bolduc, Chayne Planiden
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 infor…
Error bounds for overdetermined and underdetermined generalized centred simplex gradients
Warren Hare, Gabriel Jarry--Bolduc, Chayne Planiden
Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of poi…
A deterministic algorithm to compute the cosine measure of a finite positive spanning set
Warren Hare, Gabriel Jarry-Bolduc
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 ba…