New Inertial Projection Methods for Solving Multivalued Variational Inequality Problems Beyond Monotonicity

Abstract In this paper, we present two new inertial projection-type methods for solving multivalued variational inequality problems in finite-dimensional spaces. We establish the convergence of sequence generated by these when mapping associated with problem is only required to be locally bounded without any monotonicity assumption. Furthermore, techniques that employ paper are quite different from ones used most papers. Moreover, based on weaker assumptions factor our methods, derive several special cases methods. Finally, some experimental results illustrate profits gain introducing extrapolation steps.