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On the convergence of the Bermúdez-Moreno algorithm with constant parameters. (English) Zbl 1003.65069
Summary: A. Bermúdez and C. Moreno [Comput. Math. Appl. 7, 43-58 (1981; Zbl 0456.65036)] 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 Bermudez and 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.

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
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