Solving strongly monotone variational and quasi-variational inequalities

Nesterov, Yurii;Scrimali, Laura
(2006)

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  • Nesterov, YuriiUCLouvain
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  • Scrimali, LauraUCLouvain
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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 inequality. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutions. Moreover, we get a new numerical scheme, which rate of convergence is much higher than that of the straightforward gradient method.
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Nesterov, Y., & Scrimali, L. (2006). Solving strongly monotone variational and quasi-variational inequalities (CORE Discussion Papers 2006/107). https://hdl.handle.net/2078.5/34700