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Two numerical schemes for general variational inequalities

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  • In this paper, we compare between the forward-backward splitting method and the extra-gradient method for solving general variational inequalities. It is known that both of these methods are predictor-corrector methods. They use different search directions in the correction-step. Our analysis explains theoretically why the extra-gradient methods would be better than the forward-backward splitting methods for general variational inequalities. We suggest some new step selection procedure independent of the Lipschitz constant. This is a very desirable circumstance when the operator approximates a differential operator. We prove its convergence in Hilbert spaces of any dimension. Our proof is simple as compared with other methods.
    Mathematics Subject Classification: Primary: 65K05, 90C33; Secondary: 65K10.

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