Abstract
The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the generalized D-gap function. Recently, a hybrid Newton-type method was proposed by Peng and Fukushima for minimizing a special form of the generalized D-gap function. In this paper, the hybrid Newton-type algorithm is extended to minimize the general form gab of the generalized D-gap function. It is shown that the algorithm has nice convergence properties. Under some reasonable conditions, it is proved that the algorithm is locally and globally convergent. Moreover, it is proved that the function gab has bounded level sets for strongly monotone VIP. An error bound of the algorithm is obtained.
© 2003 Plenum Publishing Corporation
© 2003 Plenum Publishing Corporation
| Original language | English |
|---|---|
| Pages (from-to) | 535-552 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 119 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Dec 2003 |
| 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
This project was supported by Strategic Research Grant 7001427 of the City University of Hong Kong and by Grant 10171055 of the National Natural Science Foundation of China.
Research Keywords
- Error bound estimation
- Generalized D-gap function
- Global convergence
- Unconstrained optimization
- Variational inequality problems
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