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

TL;DR

This paper introduces a MATLAB software implementation of the SC-SR1 method for efficiently solving large-scale trust-region subproblems using limited-memory L-SR1 matrices and shape-changing norms, demonstrating high accuracy and competitive performance.

Contribution

The paper presents a novel MATLAB implementation of the SC-SR1 method that leverages shape-changing norms to solve trust-region subproblems with L-SR1 matrices, including the hard case.

Findings

High-accuracy solutions to trust-region subproblems, even in the hard case.

Competitive performance compared to truncated CG solver.

Effective handling of large-scale optimization problems.

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.