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arXiv · 2209.12057

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

Johannes J. Brust·Jennifer B. Erway·Roummel F. Marcia
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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.

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BibTeXRIS

Johannes J. Brust, Jennifer B. Erway, Roummel F. Marcia. 2022-09-24. Shape-Changing Trust-Region Methods Using Multipoint Symmetric Secant Matrices. https://arxiv.org/abs/2209.12057

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