Sharp Penalty Mappings for Variational Inequality Problems

First, this paper introduces a notion of a sharp penalty mapping which can replace more common exact penalty function for convex feasibility problems. Second, it uses it for solution of variational inequalities with monotone operators or pseudo-varitional inequalities with oriented operators. Appropriately scaled the sharp penalty mapping can be used as an exact penalty in variational inequalities to turn them into fixed point problems. Then they can be approximately solved by simple iteration method.