# Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices

arXiv: https://arxiv.org/abs/2209.12057 · HTML: https://mlsanity.com/paper/2209.12057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2022.

## Built on by (most cited first, 1 of 1)

- [Useful Compact Representations for Data-Fitting](https://mlsanity.com/paper/2403.12206/) (2024)

## Abstract (arXiv)

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.