Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities |
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| Authors: | Jean-Pierre Crouzeix Patrice Marcotte Daoli Zhu |
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| Affiliation: | (1) LIMOS, Université Blaise Pascal, 63177 Aubière Cedex, France, e-mail: crouzeix@ucfma.univ-bpclermont.fr, FR;(2) DIRO, Université de Montréal, C.P. 6128, succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7, e-mail: marcotte@iro.umontreal.ca, CA;(3) CRT, Université de Montréal, C.P. 6128, succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7, e-mail: daoli@crt.umontreal.ca, CA |
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| 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 conditions 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 natural way, new and useful notions of generalized monotonicity for which first order characterizations are presented. Received: September 25, 1997 / Accepted: March 2, 1999?Published online July 20, 2000 |
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| Keywords: | : variational inequalities – cutting planes – generalized monotonicity |
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