American Institute of Mathematical Sciences

December  2011, 31(4): 1383-1396. doi: 10.3934/dcds.2011.31.1383

Solving strongly monotone variational and quasi-variational inequalities

 1 Center for Operations Research and Econometrics (CORE), Catholic University of Louvain, 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium 2 Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania

Received  November 2009 Revised  September 2010 Published  September 2011

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequalities. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutions. Moreover, we get a new numerical scheme, whose rate of convergence is much higher than that of the straightforward gradient method.
Citation: Yurii Nesterov, Laura Scrimali. Solving strongly monotone variational and quasi-variational inequalities. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1383-1396. doi: 10.3934/dcds.2011.31.1383
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