194 citations · 422 across the 29 of their papers we have counts for
31 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…
Expected decrease for derivative-free algorithms using random subspaces
Warren Hare, Lindon Roberts, Clément W. Royer
Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, the…
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…
A matrix algebra approach to approximate Hessians
W. Hare, G. Jarry-Bolduc, C. Planiden
This work presents a novel matrix-based method for constructing an approximation Hessian using only function evaluations. The method requires less computational power than interpol…
Detecting negative eigenvalues of exact and approximate Hessian matrices in optimization
Warren Hare, Clément W. Royer
Nonconvex minimization algorithms often benefit from the use of second-order information as represented by the Hessian matrix. When the Hessian at a critical point possesses negati…
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…