title: On the convergence of the Bermudez-Moreno algorithm with constant parameters
abstract: A. Bermudez and C. Moreno (1981) presented a duality numerical algorithm for solving variational inequalities of the second kind. The performance of this algorithm strongly depends on the choice of two constant parameters. Assuming a further hypothesis of the inf-sup type, we present here a convergence theorem that improves on the one presented by A. Bermudez and C. Moreno. We prove that the convergence is linear, and we give the expression of the asymptotic error constant and the explicit form of the optimal parameters, as a function of some constants related to the variational inequality. Finally, we present some numerical examples that confirm the theoretical results
keyphrases: Bermudez-Moreno algorithm constant parameters duality numerical algorithm variational inequalities convergence theorem asymptotic error constant optimal parameters