Algorithm 1030: SC-SR1: MATLAB Software for Limited-memory SR1 Trust-region Methods

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 conjugate-gradients.