Shape-Changing L-SR1 Trust-Region Methods
2016 (English)Report (Other academic)
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.
large-scale optimization, limited-memory algorithms, trust-region algorithms, symmetric rank-one updates
IdentifiersURN: urn:nbn:se:liu:diva-130633OAI: oai:DiVA.org:liu-130633DiVA: diva2:953957