Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1093.90085
Hager, William W.; Zhang, Hongchao
A new conjugate gradient method with guaranteed descent and an efficient line search.
(English)
[J] SIAM J. Optim. 16, No. 1, 170-192 (2005). ISSN 1052-6234; ISSN 1095-7189/e

Summary: A new nonlinear conjugate gradient method and an associated implementation, based on an inexact line search, are proposed and analyzed. With exact line search, our method reduces to a nonlinear version of the Hestenes--Stiefel conjugate gradient scheme. For any (inexact) line search, our scheme satisfies the descent condition ${\bold g}_k^{T} {\bold d}_k \le-\frac{7}{8}\|{\bold g}_k\|^2$. Moreover, a global convergence result is established when the line search fulfills the Wolfe conditions. A new line search scheme is developed that is efficient and highly accurate. Efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer. High accuracy is achieved by using a convergence criterion, which we call the approximate Wolfe'' conditions, obtained by replacing the sufficient decrease criterion in the Wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion. Numerical comparisons are given with both L-BFGS and conjugate gradient methods using the unconstrained optimization problems in the CUTE library.
[Klaus Schittkowski (Bayreuth)]
MSC 2000:
*90C52 Methods of reduced gradient type
90C06 Large-scale problems

Keywords: conjugate gradient method; unconstrained optimization; convergence; line search; Wolfe conditions; nonlinear programming; global convergence; CUTE

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster