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Shape-Changing L-SR1 Trust-Region Methods
Applied Mathematics, University of California, Merced, USA.
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-1836-4200
Department of Mathematics, Wake Forest University, USA.
Applied Mathematics, University of California, Merced, USA.
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2016 (English)Report (Other academic)
Abstract [en]

In this article, we propose a method for solving the trust-region subproblem when a limited-memory symmetric rank-one matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms to decompose the trust-region subproblem into two separate problems, one of which has a closed-form solution and the other one is easy to solve. Sufficient conditions for global solutions to both subproblems are given. The proposed solver makes use of the structure of limited-memory symmetric rank-one matrices to find solutions that satisfy these optimality conditions. Solutions to the trust-region subproblem are computed to high-accuracy even in the so-called "hard case".

Place, publisher, year, edition, pages
Cornell University: arXiv.org , 2016. , 14 p.
Keyword [en]
large-scale optimization, limited-memory algorithms, trust-region algorithms, symmetric rank-one updates
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-130633OAI: oai:DiVA.org:liu-130633DiVA: diva2:953957
Available from: 2016-08-19 Created: 2016-08-19 Last updated: 2016-08-23Bibliographically approved

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Shape-Changing L-SR1 Trust-Region Methods(208 kB)12 downloads
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Link to original full text at arxiv.org

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Burdakov, Oleg
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Optimization Faculty of Science & Engineering
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