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On Solving L-SR1 Trust-Region Subproblems

Johannes Brust (jbrust***at***ucmerced.edu)
Jennifer Erway (erwayjb***at***wfu.edu)
Roummel Marcia (rmarcia***at***ucmerced.edu)

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 sub- problems. 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

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Optimization Software and Modeling Systems

Citation: Technical Report 2015-1, Wake Forest University, 2015

Download: [PDF]

Entry Submitted: 06/18/2015
Entry Accepted: 06/18/2015
Entry Last Modified: 08/12/2016

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