Geodesic
A representation of functions of several variables as the difference of convex functions
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 36-65 
V. A. Zalgaller. A representation of functions of several variables as the difference of convex functions. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 36-65. http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a2/
@article{ZNSL_1997_246_a2,
     author = {V. A. Zalgaller},
     title = {A representation of functions of several variables as the difference of convex functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {36--65},
     year = {1997},
     volume = {246},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a2/}
}
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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.