BibTeX
@ARTICLE{
Gundersen2012Sih,
author = "Gundersen, Geir and Steihaug, Trond",
title = "Sparsity in higher order methods for unconstrained optimization",
journal = "Optimization Methods and Software",
volume = "27",
number = "2",
pages = "275294",
year = "2012",
doi = "10.1080/10556788.2011.597853",
url = "http://www.tandfonline.com/doi/abs/10.1080/10556788.2011.597853",
eprint = "http://www.tandfonline.com/doi/pdf/10.1080/10556788.2011.597853",
abstract = "In this paper, we introduce data structures for storing the third derivative
(tensor) of a multivariate scalar function when the second and third derivatives of the function are
sparse. We consider solving unconstrained optimization problems using methods of the Halley class.
The gradient, Hessian matrix and the tensor of the objective function are required for the methods
and they have a thirdorder rate of convergence. However, these methods require the solution of two
linear systems of equations at each iteration. Solving the linear systems using a factorization will
cause fillins. The impact of these fillins will be discussed and we give the number of arithmetic
operations of the methods of the Halley class compared to Newton's method. Finally, we will
give some preliminary numerical results showing that including the time to compute the derivatives,
the ratios of elapsed time of methods in the Halley class and Newton's method are close to the
ratios of arithmetic operations.",
ad_theotech = "Higher Order, Sparsity"
}
