Abstract
In this paper, we deal with matrix-free preconditioners for nonlinear conjugate gradient (NCG) methods. In particular, we review proposals based on quasi-Newton updates, and either satisfying the secant equation or a secant-like equation at some of the previous iterates. Conditions are given proving that, in some sense, the proposed preconditioners also approximate the inverse of the Hessian matrix. In particular, the structure of the preconditioners depends both on low-rank updates along with some specific parameters. The low-rank updates are obtained as by-product of NCG iterations. Moreover, we consider the possibility to embed damped techniques within a class of preconditioners based on quasi-Newton updates. Damped methods have proved to be effective to enhance the performance of quasi-Newton updates, in those cases where the Wolfe linesearch conditions are hardly fulfilled. The purpose is to extend the idea behind damped methods also to improve NCG schemes, following a novel line of research in the literature. The results, which summarize an extended numerical experience using large-scale CUTEst problems, is reported, showing that these approaches can considerably improve the performance of NCG methods.
Original language | English |
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Title of host publication | Numerical Analysis and Optimization - NAO-IV, 2017 |
Editors | Lucio Grandinetti, Mehiddin Al-Baali, Anton Purnama |
Publisher | Springer New York LLC |
Pages | 1-21 |
Number of pages | 21 |
Volume | 235 |
ISBN (Print) | 9783319900254 |
DOIs | |
Publication status | Published - 2018 |
Event | 4th International Conference on Numerical Analysis and Optimization, NAO-IV 2017 - Muscat, Oman Duration: Jan 2 2017 → Jan 5 2017 |
Other
Other | 4th International Conference on Numerical Analysis and Optimization, NAO-IV 2017 |
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Country/Territory | Oman |
City | Muscat |
Period | 1/2/17 → 1/5/17 |
Keywords
- Conjugate gradient method
- Damped techniques
- Large scale unconstrained optimization
- Nonlinear conjugate gradient methods
- Preconditioning
- Quasi-Newton methods
ASJC Scopus subject areas
- Mathematics(all)