On the convergence of the Bermúdez-Moreno algorithm with constant parameters

Summary. Bermúdez-Moreno 5] presents 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 in 5]: 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. Received June 28, 1999 / Revised version received February 19, 2001 / Published online October 17, 2001