  We give a simple alternative proof for the $C^{1,1}$--convex extension
problem which has been introduced and studied by D. Azagra and C. Mudarra [2].
As an application, we obtain an easy constructive proof for the Glaeser-Whitney
problem of $C^{1,1}$ extensions on a Hilbert space. In both cases we provide
explicit formulae for the extensions. For the Gleaser-Whitney problem the
obtained extension is almost minimal, that is, minimal up to a factor
$\frac{1+\sqrt{3}}{2}$ in the sense of Le Gruyer [15].
