A representation of functions of several variables as the difference of convex functions

If a function $f\colon D^n\to \mathbb R$, where $D^n$ is a convex compact set in $\mathbb R^n$, admits a decomposition $f=g-h$ with convex $g,h$ where $h$ is upper bounded, then there exists such a decomposition which is in some sense “minimal”. A recurrent procedure converging to that decomposition is given. For piecewise linear functions $f$, finite algorithms of those decompositions for $n=1,2$ are given. A number of examples clarifying some unexpected effects is represented. Problems are formulated.