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The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the D-gap function. It is proved that the D-gap function has bounded level sets for the strongly monotone VIP. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under some conditions, it is shown that the algorithm is(More)
The Karush-Kuhn-Tucker (KKT) conditions can be regarded as optimality conditions for both variational inequalities and constrained optimization problems. In order to overcome some drawbacks of recently proposed reformulations of KKT systems, we propose to cast KKT systems as a minimization problem with nonnegativity constraints on some of the variables. We(More)
A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also(More)
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