Preprint A611/2008
A strongly convergent direct method for monotone variational inequalities in Hilbert spaces
Alfredo Iusem | J.Y. Bello Cruz
Keywords: Monotone variational inequaliies | maximal monotone operator | projetion method

We introduce a two-step direct method, like Korpelevich's, for solving monotone variational inequalities. The advantage of our method over that one is that ours converges strongly in Hilbert spaces, while only weak convergence has been proved for Korpelevich's algorithm. Our method also has the following desirable property: the sequence converges to the solution of the problem which lies closest to the initial iterate.