5 papers
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…