Representation of piecewise affine functions as a difference of polyhedral

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.