A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem

Abstract

The trust-region subproblem arises frequently in linear algebra and optimization applications. Recently, matrix-free methods have been introduced to solve large-scale trust-region subproblems. These methods only require a matrix-vector product and do not rely on matrix factorizations [4, 7]. These approaches recast, the trust region subproblem% in terms of a parametrized eigenvalue problem and then adjust the parameter to find the optimal solution from the eigenvector corresponding to the smallest eigenvalue of the parametrized eigenvalue problem. This paper presents a new matrix-free algorithm for the large-scale trust-region subproblem. The new algorithm improves upon the previous algorithms by introducing a unified iteration that naturally includes the so called hard case. The new iteration is shown to be superlinearly convergent in all cases. Computational results are presented to illustrate convergence properties and robustness of the method.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1995
Accession Number
ADA445632

Entities

People

  • Danny C. Sorensen
  • Sandra A. Santos

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algebra
  • Algorithms
  • Applied Mathematics
  • Eigenvalues
  • Eigenvectors
  • Heuristic Methods
  • Information Operations
  • Iterations
  • Linear Algebra
  • Mathematics
  • Operations Research

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation
  • Operations Research