Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices
Optimization and Control
2022-10-11 v2
Abstract
In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized multipoint symmetric secant (MSS) matrices to approximate the Hessian. Shape-changing norms and dense initializations have been successfully used in the context of traditional quasi-Newton methods, but have yet to be explored in the case of MSS methods. Numerical results suggest that trust-region methods that use densely-initialized MSS matrices together with shape-changing norms outperform MSS with other trust-region methods.
Cite
@article{arxiv.2209.12057,
title = {Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices},
author = {Johannes J. Brust and Jennifer B. Erway and Roummel F. Marcia},
journal= {arXiv preprint arXiv:2209.12057},
year = {2022}
}