A Strongly Convergent Direct Method for Monotone Variational Inequalities in Hilbert Spaces |
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Authors: | J Y Bello Cruz A N Iusem |
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Institution: | 1. Instituto de Matemática Pura e Aplicada , Rio de Janeiro, Brazil yunier@impa.br;3. Instituto de Matemática Pura e Aplicada , Rio de Janeiro, Brazil |
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Abstract: | 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, whereas 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 that lies closest to the initial iterate. |
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Keywords: | Armijo-type search Korpelevich's method Maximal monotone operators Monotone variational inequalities Projection method Strong convergence |
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