IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-18T13:48:33Z EPrints http://eprints.imtlucca.it/images/logowhite.png http://eprints.imtlucca.it/ 2011-07-27T09:32:44Z 2014-07-17T12:39:20Z http://eprints.imtlucca.it/id/eprint/468 This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/468 2011-07-27T09:32:44Z Convexity recognition of the union of polyhedra In this paper we consider the following basic problem in polyhedral computation: Given two polyhedra in Rd, P and Q, decide whether their union is convex, and, if so, compute it. We consider the three natural specializations of the problem: 1) when the polyhedra are given by halfspaces (H-polyhedra), 2) when they are given by vertices and extreme rays (V-polyhedra), and 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 strongly-polynomially solvable. Alberto Bemporad alberto.bemporad@imtlucca.it Komei Fukuda Fabio Danilo Torrisi 2011-07-27T09:11:28Z 2014-07-17T12:18:14Z http://eprints.imtlucca.it/id/eprint/571 This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/571 2011-07-27T09:11:28Z On convexity recognition of the union of polyhedra 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. Alberto Bemporad alberto.bemporad@imtlucca.it Komei Fukuda Fabio Danilo Torrisi