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