Solving box constrained variational inequalities by using the natural residual with D-gap function globalization

Authors:
Christian Kanzow;Masao Fukushima
Affiliations:
Institute of Applied Mathematics, University of Hamburg, Bundesstrasse 55, D-20146 Hamburg, Germany;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Operations Research Letters
Year:
1998

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Abstract

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.