  In this paper we introduce a technique to produce tighter cutting planes for
mixed-integer non-linear programs. Usually, a cutting plane is generated to cut
off a specific infeasible point. The underlying idea is to use the infeasible
point to restrict the feasible region in order to obtain a tighter domain. To
ensure validity, we require that every valid cut separating the infeasible
point from the restricted feasible region is still valid for the original
feasible region. We translate this requirement in terms of the separation
problem and the reverse polar. In particular, if the reverse polar of the
restricted feasible region is the same as the reverse polar of the feasible
region, then any cut valid for the restricted feasible region that separates
the infeasible point, is valid for the feasible region. We show that the
reverse polar of the visible points of the feasible region from the infeasible
point coincides with the reverse polar of the feasible region. In the special
where the feasible region is described by a single non-convex constraint
intersected with a convex set we provide a characterization of the visible
points. Furthermore, when the non-convex constraint is quadratic the
characterization is particularly simple. We also provide an extended
formulation for a relaxation of the visible points when the non-convex
constraint is a general polynomial. Finally, we give some conditions under
which for a given set there is an inclusion-wise smallest set, in some
predefined family of sets, whose reverse polars coincide.
