3 citations · 3 across the 13 of their papers we have counts for
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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…
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…
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…
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…
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…