Abstract
Quasi-Newton (QN) equation plays a core role in contemporary nonlinear optimization. The usual QN equation employs only the gradients, but ignores the available function value information. In this paper, we derive a class of modified QN equations with a vector parameter which use both available gradient and function value information. The modified quasi-Newton methods maintain most properties of the usual quasi-Newton methods, meanwhile they achieve a higher-order accuracy in approximating the second-order curvature of the problem functions than the usual ones do. Numerical experiments are reported which support the theoretical analyses and show the advantages of the modified QN methods over the usual ones. © 2001 Elsevier Science B.V. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 269-278 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 137 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Dec 2001 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Funding
The research is partially supported by City University of Hong Kong under its Strategic Research Grant #7000944 and the National Natural Science Foundation of China.
Research Keywords
- Broyden family of updates
- Curvature approximation
- Positive-definite update
- Quasi-Newton equation
- Superlinear convergence
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