Title: ON CANONICAL REPRESENTATIONS OF CONVEX POLYHEDRA
Abstract: Mathematical Software, pp. 350-360 (2002) No AccessON CANONICAL REPRESENTATIONS OF CONVEX POLYHEDRADAVID AVIS, KOMEI FUKUDA and STEFANO PICOZZIDAVID AVISSchool Of Computer Science, MGill University, Canada, KOMEI FUKUDASchool Of Computer Science, MGill University, Canada and STEFANO PICOZZIInstitute of Mathematics, EPFL, Switzerlandhttps://doi.org/10.1142/9789812777171_0037Cited by:12 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: Every convex polyhedron in the Euclidean space ℝd admits both H-representation and V-representation. When working with convex polyhedra, in particular large-scale ones in high dimensions, it is useful to have a canonical representation that is minimal and unique up to some elementary operations. Such a representation allows one to compare two H-polyhedra or two V-polyhedra efficiently. In this paper, we define such representations that are simple and can be computed in polynomial time. The key ingredients are redundancy removal for linear inequality systems and affine transformations of polyhedra. FiguresReferencesRelatedDetailsCited By 12Converting of Boolean Expression to Linear Equations, Inequalities and QUBO Penalties for CryptanalysisAleksey I. Pakhomchik, Vladimir V. Voloshinov, Valerii M. Vinokur and Gordey B. Lesovik21 January 2022 | Algorithms, Vol. 15, No. 2On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approachMirko Pasquini and David Angeli18 November 2021 | Journal of Mathematical Biology, Vol. 83, No. 6-7On Convergence for Piecewise Affine Models of Gene Regulatory Networks via a Lyapunov ApproachMirko Pasquini and David Angeli1 Aug 2020 | IEEE Transactions on Automatic Control, Vol. 65, No. 8What Is So Special about Quantum Clicks?Karl Svozil28 May 2020 | Entropy, Vol. 22, No. 6Linear Complementarity Systems and Cone-Copositive Lyapunov StabilityL. Iannelli, R. Iervolino and F. Vasca1 Oct 2019 | IEEE Control Systems Letters, Vol. 3, No. 4On piecewise quadratic Lyapunov functions for piecewise affine models of gene regulatory networksMirko Pasquini and David Angeli1 Dec 2018Piecewise quadratic stability of consensus in heterogeneous opinion dynamicsRaffaele Iervolino, Domenico Tangredi and Francesco Vasca1 Jun 2016Complexity Analysis of Continuous Petri NetsEstíbaliz Fraca and Serge Haddad1 Jan 2013Sensor Selection in Arbitrary DimensionsV. Isler and M. Magdon-Ismail1 Oct 2008 | IEEE Transactions on Automation Science and Engineering, Vol. 5, No. 4Timed Discrete Event Control of Parallel Production Lines with Continuous OutputsStephanie Geist, Dmitry Gromov and Jörg Raisch15 August 2007 | Discrete Event Dynamic Systems, Vol. 18, No. 2Efficient computation of state space over approximation of preemptive real time systemsA. Abdelli and D. Yahiatene1 Mar 2008An Efficient Method for Computing Exact State Space of Petri Nets With StopwatchesMorgan Magnin, Didier Lime and Olivier (H.) Roux1 Feb 2006 | Electronic Notes in Theoretical Computer Science, Vol. 144, No. 3 Mathematical SoftwareMetrics History PDF download