  Solutions of a variational inequality are found by giving conditions for the
monotone convergence with respect to a cone of the Picard iteration
corresponding to its natural map. One of these conditions is the isotonicity of
the projection onto the closed convex set in the definition of the variational
inequality. If the closed convex set is a cylinder and the cone is an extented
Lorentz cone, then this condition can be dropped because it is automatically
satisfied. The obtained result is further particularized for unbounded box
constrained variational inequalities. For this case a numerical example is
presented.
