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arXiv · 1607.03533

Algorithm XXX: SC-SR1: Matlab software for solving shape-changing L-SR1 trust-region subproblems

Johannes Brust·Oleg Burdakov·Jennifer B. Erway·Roummel F. Marcia·Ya-Xiang Yuan
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Abstract

We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region. subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix, which can be used for large-scale optimization. The method takes advantage of two shape-changing norms[Burdakov and Yuan 2002; Burdakov et al. 2017] to decompose the trust-region subproblem into two separate problems. Using one of the proposed norms, the resulting subproblems have closed-form solutions. Meanwhile, using the other proposed norm, one of the resulting subproblems has a closed-form solution while the other is easily solvable using techniques that exploit the structure of L-SR1 matrices. Numerical results suggest that the SC-SR1 method is able to solve trust-region subproblems to high accuracy even in the so-called "hard case". When integrated into a trust-region algorithm, extensive numerical experiments suggest that the proposed algorithms perform well, when compared with widely used solvers, such as truncated CG.

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Johannes Brust, Oleg Burdakov, Jennifer B. Erway, Roummel F. Marcia, Ya-Xiang Yuan. 2016-07-12. Algorithm XXX: SC-SR1: Matlab software for solving shape-changing L-SR1 trust-region subproblems. https://arxiv.org/abs/1607.03533

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