A Smooth Dual Gap Function Solution to a Class of Quasivariational Inequalities

The aim of this paper is to construct a regularization of a gap function solution to a quasivariational inequality problem. The regularization may happen for example, by means of Toland’s and Singer’s duality theory for d.c. functions and lead to an everywhere finite and smooth dual gap function. The corresponding Fr´echet derivative of the dual gap function is calculable from the data of the quasivariational inequality problem