Solving strongly monotone variational and quasi-variational inequalities
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.
|Date of creation:||00 Dec 2006|
|Date of revision:|
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- Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, 01.
- Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
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