Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities

The D-gap function, recently introduced by Peng and further studied by Yamashita et al., allows a smooth unconstrained minimization reformulation of the general variational inequality problem. This paper is concerned with the D-gap function for variational inequality problems over 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 points, bounded level sets, global error bounds and generalized Hessians. Next we present a nonsmooth Gauss-Newton type algorithm for minimizing the D-gap function, and report extensive numerical results for the whole set of problems in the MCPLIB test problem collection. The work of this author was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, Japan.