Practical Convergence Conditions for Restarted Conjugate Gradient Methods.

Abstract

OREMS, Optimization*Conjugate gradient methods, EigenvaluesConvergence properties of restarted conjugate gradient methods are investigated for the case where the usual requirement that an exact line search be performed at each iteration is relaxed. The objective function is assumed to have continuous second derivatives and the eigenvalues of the Hessian are assumed to be bounded above and below by positive constants. It is further assumed that a Lipschitz condition on the second derivatives is satisfied at the location of the minimum. A class of descent methods is described which exhibit n-step quadratic convergence when restarted even though errors are permitted in the line search. It is then shown that two conjugate gradient methods belong to this class. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1973
Accession Number
AD0774248

Entities

People

  • Melanie L. Lenard

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Convergence
  • Differential Equations
  • Eigenvalues
  • Iterations
  • Mathematical Analysis
  • Mathematics
  • Optimization

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research