# On convexity recognition of the union of polyhedra

Bemporad, Alberto and Fukuda, Komei and Torrisi, Fabio Danilo On convexity recognition of the union of polyhedra. In: International Conference on Advances in Convex Analysis and Global Optimization, June 5-9, 2000, Samos, Greece pp. 64-65. (2000)

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## Abstract

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.

Item Type: Conference or Workshop Item (Paper) Q Science > QA Mathematics Computer Science and Applications Professor Alberto Bemporad 27 Jul 2011 09:11 17 Jul 2014 12:18 http://eprints.imtlucca.it/id/eprint/571