English

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.

Keywords

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}
}
R2 v1 2026-06-28T02:01:37.130Z