A QP-free constrained Newton-type method for variational inequality problems

Authors
Citation
C. Kanzow et Hd. Qi, A QP-free constrained Newton-type method for variational inequality problems, MATH PROGR, 85(1), 1999, pp. 81-106
Citations number
36
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610 → ACNP
Volume
85
Issue
1
Year of publication
1999
Pages
81 - 106
Database
ISI
SICI code
0025-5610(199905)85:1<81:AQCNMF>2.0.ZU;2-L
Abstract
We consider a simply constrained optimization reformulation of the Karush-R uhn-Tucker conditions arising from variational inequalities. Based on this reformulation, we present a new Newton-type method for the solution of vari ational inequalities. The main properties of this method are: (a) it is wel l-defined for an arbitrary variational inequality problem, (b) it is global ly convergent at least to a stationary point of the constrained reformulati on, (c) it is locally superlinearly/quadratically convergent under a certai n regularity condition, (d) all iterates remain feasible with respect to th e constrained optimization reformulation, and (e) it has to solve just one linear system of equations at each iteration. Some preliminary numerical re sults indicate that this method is quite promising.