Geodesic
Representation of piecewise affine functions as a difference of polyhedral
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2016), pp. 4-18

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The problem of representation of any analytic expression of a piecewise affine function as a sum of a convex and a concave polyhedral function, or an equivalent difference of two convex (d.c.) polyhedral functions, is observed. Two algorithms, solving this problem, are proposed. The first algorithm reconstructs a piecewise affine function using its codifferential mapping and the function’s value at a point. The second algorithm provides direct conversion of a piecewise affine function into a sum of a convex and a concave polyhedral functions. Refs 39. Figs 4.
Keywords: piecewise affine function, representation, d.c. functions, codifferential. 
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T. A. Angelov. Representation of piecewise affine functions as a difference of polyhedral. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2016), pp. 4-18. http://geodesic.mathdoc.fr/item/VSPUI_2016_1_a0/