Solving box constrained variational inequalities by using the natural residual with D-gap function globalization. (English) Zbl 0941.90070

Summary: We present a new method for the solution of the Box constrained Variational Inequality Problem (BVIP). Basically, this method is a nonsmooth Newton method applied to a reformulation of BVIP as a system of nonsmooth equations involving the natural residual. The method is globalized by using the D-gap function. We show that the proposed algorithm is globally and fast locally convergent. Moreover, if the problem is described by an affine function, the algorithm has a finite termination property. Numerical results for some large-scale variational inequality problems are reported.


90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C53 Methods of quasi-Newton type
65K10 Numerical optimization and variational techniques


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