  Recently, Kronqvist et al.~\cite{KronqvistLundellWesterlund2016} rediscovered
the supporting hyperplane algorithm of Veinott~\cite{Veinott1967} and
demonstrated its computational benefits for solving convex mixed-integer
nonlinear programs.
  In this paper we derive the algorithm from a geometric point of view.
  This enables us to show that the supporting hyperplane algorithm is
equivalent to Kelley's cutting plane algorithm~\cite{J.E.Kelley1960} applied to
a particular reformulation of the problem.
  As a result, we extend the applicability of the supporting hyperplane
algorithm to convex problems represented by general, not necessarily convex,
differentiable functions that satisfy a mild condition.
