Applied mathematics

Representation of piecewise affine functions as a difference of polyhedral

T. A. Angelov

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russia

Abstract: 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.

UDC: 519.6

Received: November 26, 2015

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