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Shape-Changing L-SR1 Trust-Region Methods

Johannes Brust(jbrust***at***ucmerced.edu)
Oleg Burdakov(oleg.burdakov***at***liu.se)
Jennifer Erway(erwayjb***at***wfu.edu)
Roummel Marcia(rmarcia***at***ucmerced.edu)
Ya-xiang Yuan(yyx***at***lsec.cc.ac.cn)

Abstract: 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”.

Keywords: Large-scale unconstrained optimization, nonconvex optimization, trust-region methods, limited-memory quasi-Newton methods, symmetric rank-one update, shape-changing norm

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report 2016-2, Wake Forest University, Department of Mathematics, 2016.

Download: [PDF]

Entry Submitted: 07/12/2016
Entry Accepted: 07/12/2016
Entry Last Modified: 07/12/2016

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