  Given a nonlinear, univariate, bounded, and differentiable function $f(x)$,
this article develops a sequence of Mixed Integer Linear Programming (MILP) and
Linear Programming (LP) relaxations that converge to the graph of $f(x)$ and
its convex hull, respectively. Theoretical convergence of the sequence of
relaxations to the graph of the function and its convex hull is established.
For nonlinear non-convex optimization problems, the relaxations presented in
this article can be used to construct tight MILP and LP relaxations. These MILP
and the LP relaxations can also be used with MILP-based and spatial
branch-and-bound based global optimization algorithms, respectively.
