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On Convexity Recognition of the Union of Polyhedra


A. Bemporad, K. Fukuda, F.D. Torrisi

International Conference on Advances in Convex Analysis and Global Optimization, Samos, Greece, pp. 82,83

In this paper we consider the following basic problem in polyhedral computation: Given two polyhedra in $R^d$, $P$ and $Q$, decide whether their union is convex, and eventually compute it. We consider the three natural specializations of the problem: (1) when the polyhedra are given by half-spaces (H-polyhedra) (2) when they are given by vertices and extreme rays (V-polyhedra) (3) when both H- and V-polyhedral representations are available. Both the bounded (polytopes) and the unbounded case are considered. We show that the first two problems are polynomially solvable, and that the third problem is solvable in linear time.

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% Autogenerated BibTeX entry
@InProceedings { BemFuk:2000:IFA_330,
    author={A. Bemporad and K. Fukuda and F.D. Torrisi},
    title={{On Convexity Recognition of the Union of Polyhedra}},
    booktitle={International Conference on Advances in Convex Analysis and
	  Global Optimization},
    address={Samos, Greece},
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