6 citations · 14 across the 18 of their papers we have counts for
19 papers
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…
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…
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…
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…