Algorithm 1030: SC-SR1: MATLAB Software for Limited-memory SR1 Trust-region Methods
2022 (English)In: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 48, no 4, article id 48Article in journal (Refereed) Published
Abstract [en]
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 et al. 2017; Burdakov and Yuan 2002] 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 solutionwhile 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.
Place, publisher, year, edition, pages
ASSOC COMPUTING MACHINERY , 2022. Vol. 48, no 4, article id 48
Keywords [en]
Large-scale unconstrained optimization; trust-region methods; limited-memory quasi-Newton methods; symmetric rank-one update; shape-changing norm
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-192962DOI: 10.1145/3550269ISI: 000952026200012OAI: oai:DiVA.org:liu-192962DiVA, id: diva2:1750113
Note
Funding Agencies|National Science Foundation [CMMI-1333326, CMMI-1334042, IIS-1741264, IIS-1741490]; U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR) [DE-AC02-06CH11347]
2023-04-122023-04-122023-04-12