In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These
variational inequalities include as special cases, the previously known
classes of variational inequalities. Using projection techniques, we show
that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used
to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to
study the existence of a solution of multivalued variational inequalities
and suggest a novel iterative algorithm. In addition, we have shown that
the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.
On a class of multivalued variational inequalities
