Some methods based on the D-gap function for solving monotone variational inequalities

The D-gap function has been useful in developing unconstrained descent meth ods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for mon otone variational inequality problems with bounded feasible set. Accordingl y, we develop two unconstrained methods based on them that are similar in s pirit to a feasible method of Zhu and Marcotte based on the regularized-gap function. We further discuss a third method based on applying the D-gap fu nction to a regularized problem. Preliminary numerical experience is also r eported.