MSS: MATLAB Software for L-BFGS Trust-Region Subproblems for Large-Scale Optimization

A MATLAB implementation of the More-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More-Sorensen direct method into...

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Bibliographic Details
Main Authors Erway, Jennifer B, Marcia, Roummel F
Format Journal Article
LanguageEnglish
Published 06.12.2012
Subjects
Mathematics - Numerical Analysis
Mathematics - Optimization and Control
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DOI10.48550/arxiv.1212.1525

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Summary:A MATLAB implementation of the More-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the More-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed stable fast direct method for solving large shifted BFGS systems of equations [13, 12] and is able to compute solutions to any user-defined accuracy. This MATLAB implementation is a matrix-free iterative method for large-scale optimization. Numerical experiments on the CUTEr [3, 16]) suggest that using the MSS method as a trust-region subproblem solver can require significantly fewer function and gradient evaluations needed by a trust-region method as compared with the Steihaug-Toint method.
Bibliography:Technical Report 2012-5, Wake Forest University
DOI:10.48550/arxiv.1212.1525