an:01347299
Zbl 0941.90070
Kanzow, Christian; Fukushima, Masao
Solving box constrained variational inequalities by using the natural residual with D-gap function globalization
EN
Oper. Res. Lett. 23, No. 1-2, 45-51 (1998).
0167-6377
1998
j
90C33 90C53 65K10
variational inequality problem; mixed complementarity problem; natural residual; D-gap function; Newton's method; global convergence; quadratic convergence; finite termination
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.