Review of scaling matrices
The essential properties of a scaling matrix are reviewed, with several well-known matrices from the literature.
Abstract
A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.
Method
A new scaling matrix
A new matrix is defined as the convex combination of the reviewed matrices, inheriting their properties and satisfying additional requirements.
Numerical experiments
Experiments on several important test problems demonstrate the superiority of the new scaling matrix.
Resources
- Preprint
- arXiv:1904.09209
BibTeX
@misc{ayanzadeh2019scaling,
title = {A New Class of Scaling Matrices for Scaled Trust Region Algorithms},
author = {Ayanzadeh, Aydin and Yazdanian, Shokoufeh and Shahamatnia, Ehsan},
year = {2019},
eprint = {1904.09209},
archivePrefix = {arXiv},
primaryClass = {math.OC},
url = {https://arxiv.org/abs/1904.09209}
}