Solving strongly monotone variational and quasi-variational inequalities

Nesterov, Yurii;Scrimali, Laura
(2011) Discrete and Continuous Dynamical Systems — Vol. 31, n° 4, p. 1383-1396 (2011)

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  • Nesterov, YuriiUCLouvain
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  • Scrimali, LauraUniversity di Catania
    Author
Abstract
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.
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Nesterov, Y., & Scrimali, L. (2011). Solving strongly monotone variational and quasi-variational inequalities. Discrete and Continuous Dynamical Systems, 31(4), 1383-1396. https://doi.org/10.3934/DCDS.2011.31.1383 (Original work published 2011)