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Piecewise affine functions as a difference of two convex functions. (English) Zbl 0612.26009
A function f over a convex n-dimensional polyhedral set \(B\subseteq {\mathbb{R}}^ n\) is said to be piecewise affine linear if it is continuous and if there exists both a finite decomposition \(\{B_ i\}\) of B into m convex n-dimensional polyhedral sets and some corresponding affine linear functions \(f_ i\) such that \(f(x)=f_ i(x)\) for all \(x\in B_ i,i=1,...,m.\) In the present paper two different representations of piecewise affine linear functions as differences of two convex piecewise affine linear functions are given.
Reviewer: W.W.Breckner

MSC:
26B40 Representation and superposition of functions
90C30 Nonlinear programming
26B25 Convexity of real functions of several variables, generalizations
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References:
[2] Aleksandrov A.D., Die innere Geometric der konvexen Fläehen (1955)
[3] Beer K., Lösung gro{\(\beta\)}er linearer Optiniierungsaufgaben (1977)
[4] DOI: 10.1007/BF02162405 · Zbl 0217.27602
[6] Melzer D., Mathematische Optimierung (1984)
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