On solving L-SR1 trust-region subproblems

Johannes Brust (), Jennifer B. Erway () and Roummel F. Marcia ()
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Johannes Brust: University of California, Merced
Jennifer B. Erway: Wake Forest University
Roummel F. Marcia: University of California, Merced

Computational Optimization and Applications, 2017, vol. 66, issue 2, No 2, 245-266

Abstract: Abstract In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the Sherman–Morrison–Woodbury formula to compute global solutions to trust-region subproblems. To compute the optimal Lagrange multiplier for the trust-region constraint, we use Newton’s method with a judicious initial guess that does not require safeguarding. A crucial property of this solver is that it is able to compute high-accuracy solutions even in the so-called hard case. Additionally, the optimal solution is determined directly by formula, not iteratively. Numerical experiments demonstrate the effectiveness of this solver.

Keywords: Large-scale unconstrained optimization; Trust-region methods; Limited-memory quasi-Newton methods; Symmetric rank-one update (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-016-9868-3

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