Polynomial inequalities representing polyhedra
Polynomial inequalities representing polyhedra
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表示多面体的多项式不等式
作者：
Hartwig Bosse;M. Grötschel;M. Henk
摘要。我们的主要结论是，每个n维多边形最多可以用2n−1个多项式不等式来描述，而且这些多项式可以显式地构造。对于n维点多面体圆锥，我们证明了边界2n−2，对于任意多面体，我们用2n个多项式不等式得到了一个可构造表示。
Abstract.Our main result is that every n-dimensional polytope can be described by at most 2n−1 polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n−2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.