A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions

Authors
Citation
Hd. Qi, A regularized smoothing Newton method for box constrained variational inequality problems with P-0-functions, SIAM J OPTI, 10(2), 2000, pp. 315-330
Citations number
28
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON OPTIMIZATION
ISSN journal
10526234 → ACNP
Volume
10
Issue
2
Year of publication
2000
Pages
315 - 330
Database
ISI
SICI code
1052-6234(20000223)10:2<315:ARSNMF>2.0.ZU;2-Q
Abstract
Based on Qi, Sun, and Zhou's smoothing Newton method, we propose a regulari zed smoothing Newton method for the box constrained variational inequality problem with P-0-function (P-0 BVI). The proposed algorithm generates an in finite sequence such that the value of the merit function converges to zero . If P-0 BVI has a nonempty bounded solution set, the iteration sequence mu st be bounded. This result implies that there exists at least one accumulat ion point. Under CD-regularity, we prove that the proposed algorithm has a superlinear (quadratic) convergence rate without requiring strict complemen tarity conditions. The main feature of our global convergence results is th at we do not assume a priori the existence of an accumulation point. This a ssumption is used widely in the literature due to the possible unboundednes s of level sets of various adopted merit functions. Preliminary numerical r esults are also reported.