A continuum of solutions to variational inequality with nonlinear constraints: Existence and simplicial algorithm

In this paper, we obtain an existence theorem of a connected set of solutions to a nonlinear variational inequality with explicit nonlinear constraints. This result follows in a constructive way by designing a simplicial algorithm. The algorithm operates on a triangulation of the unbounded regions and generates a piecewise linear path of parametrized stationary points. Each point on the path is an approximate solution.