THEORETICAL AND NUMERICAL INVESTIGATION OF THE D-GAP FUNCTION FOR BOXCONSTRAINED VARIATIONAL-INEQUALITIES

The D-gap function, recently introduced by Peng and further studied by Yamashita et al., allows a smooth unconstrained minimization reformul ation of the general variational inequality problem. This paper is con cerned with the D-gap function for variational inequality problems ove r a box or, equivalently, mixed complementarity problems. The purpose of this paper is twofold. First we investigate theoretical properties in depth of the D-gap function, such as the optimality of stationary p oints, bounded level sets, global error bounds and generalized Hessian s. Next we present a nonsmooth Gauss-Newton type algorithm for minimiz ing the D-gap function, and report extensive numerical results for the whole set of problems in the MCPLIB test problem collection. (C) 1998 The Mathematical Programming Society, Inc. Published by Elsevier Scie nce B.V.