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

arXiv: https://arxiv.org/abs/1607.03533 · HTML: https://mlsanity.com/paper/1607.03533/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2016.

## Built on by (most cited first, 2 of 2)

- [Useful Compact Representations for Data-Fitting](https://mlsanity.com/paper/2403.12206/) (2024)
- [Fast and Accurate SVD-Type Updating in Streaming Data](https://mlsanity.com/paper/2509.02840/) (2025)

## Abstract (arXiv)

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.