Conjugate-Gradient Methods for Large-Scale Nonlinear Optimization.
Abstract
In this paper we discuss several recent conjugate-gradient type methods for solving large-scale nonlinear optimization problems. We demonstrate how the performance of these methods can be significantly improved by careful implementation. A method based upon iterative preconditioning will be suggested which performs reasonably efficiently on a wide variety of significant test problems. Our results indicate that nonlinear conjugate-gradient methods behave in a similar way to conjugate-gradient methods for the solution of systems of linear equations. These methods work best on problems whose Hessian matrices have sets of clustered eigenvalues. On more general problems, however, even the best method may require a prohibitively large number of iterations. We present numerical evidence that indicates that the use of theoretical analysis to predict the performance of algorithms on general problems is not straightforward. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA078713
Entities
People
- Philip Edward Gill
- Walter Murray
Organizations
- Stanford University