-

 

 

 




Optimization Online





 

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

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society