Shape-Changing L-SR1 Trust-Region Methods

Brust, JohannesApplied Mathematics, University of California, Merced, USA (författare)

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".

Burdakov, Oleg,1953-Linköpings universitet,Optimeringslära,Tekniska fakulteten(Swepub:liu)olebu87 (författare)
Erway, Jennifer B.Department of Mathematics, Wake Forest University, USA (författare)
Marcia, Roummel F.Applied Mathematics, University of California, Merced, USA (författare)
Yuan, Ya-xiangState Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China (författare)
Applied Mathematics, University of California, Merced, USAOptimeringslära (creator_code:org_t)

Av författaren/redakt...: Brust, Johannes; Burdakov, Oleg, ...; Erway, Jennifer ...; Marcia, Roummel ...; Yuan, Ya-xiang

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