Piecewise affine functions and polyhedral sets
Gorokhovik, V. V.; Zorko, O. I.; Birkhoff, G.; Gorokhovik, V. V.; Byelorussian Academy of Sciences, Institute of Mathematics; Zorko, O. I.; Byelorussian Academy of Sciences, Institute of Mathematics; Birkhoff, G.; Byelorussian Academy of Sciences, Institute of Mathematics
Журнал:
Optimization
Дата:
1994
Аннотация:
In this paper we present a number of characterizations of piecewise affine and piecewise linear functions defined on finite dimesional normed vector spaces. In particular we prove that a real-valued function is piecewise affine [resp. piecewise linear] if both its epigraph and its hypograph are (nonconvex) polyhedral sets[resp..Polyhedral cones]. Also,We show that the collection of all piecewise affine[resp.piecewise linear] functions. Furthermore, we prove that a function is piecewise affine[resp.piecewise linear] if it can be represented as a difference of two convex [resp.,sublinear] polyhedral fucntions.
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