Conditions ensuring the applicability of cutting-plane methods for solvingvariational inequalities

Authors
Crouzeix, JP Marcotte, P Zhu, DL
Citation
Jp. Crouzeix et al., Conditions ensuring the applicability of cutting-plane methods for solvingvariational inequalities, MATH PROGR, 88(3), 2000, pp. 521-539
Citations number
19
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
00255610 → ACNP
Volume
88
Issue
3
Year of publication
2000
Pages
521 - 539
Database
ISI
SICI code
0025-5610(200009)88:3<521:CETAOC>2.0.ZU;2-Y
Abstract
Let VIP(F, C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak con ditions on the mapping F that allow the development of a convergent cutting -plane framework for solving VIP(F, C). In the process we introduce, in a n atural way, new and useful notions of generalized monotonicity for which fi rst order characterizations are presented.