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Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities

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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.

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Authors and Affiliations

  1. LIMOS, Université Blaise Pascal, 63177 Aubière Cedex, France, e-mail: crouzeix@ucfma.univ-bpclermont.fr, , , , , , FR

    Jean-Pierre Crouzeix

  2. DIRO, Université de Montréal, C.P. 6128, succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7, e-mail: marcotte@iro.umontreal.ca, , , , , , CA

    Patrice Marcotte

  3. CRT, Université de Montréal, C.P. 6128, succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7, e-mail: daoli@crt.umontreal.ca, , , , , , CA

    Daoli Zhu

Authors
  1. Jean-Pierre Crouzeix
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  2. Patrice Marcotte
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  3. Daoli Zhu
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Received: September 25, 1997 / Accepted: March 2, 1999¶Published online July 20, 2000

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Crouzeix, JP., Marcotte, P. & Zhu, D. Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities. Math. Program. 88, 521–539 (2000). https://doi.org/10.1007/PL00011384

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  • DOI: https://doi.org/10.1007/PL00011384

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