An Algorithm for Finding All Vertices of Convex Polyhedral Sets

Previous article Next article An Algorithm for Finding All Vertices of Convex Polyhedral SetsM. L. BalinskiM. L. Balinskihttps://doi.org/10.1137/0109008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 A. Charnes, , W. W. Cooper and , A. Henderson, An introduction to linear programming, John Wiley & Sons Inc., New York, 1953x+74 MR0056263 0050.36806 Google Scholar2 George B. Dantzig, C. T. Koopmans, Maximization of a linear function of variables subject to linear inequalitiesActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 339–347, Chapter XXI MR0056260 0045.09802 Google Scholar3 G. B. Dantzig, , Alex Orden and , Philip Wolfe, The generalized simplex method for minimizing a linear form under linear inequality restraints, Pacific J. Math., 5 (1955), 183–195 MR0069584 0064.39402 CrossrefGoogle Scholar4 R. E. Gomory, An Algorithm for Integer Solutions to Linear Programs, Technical Report No. 1, Princeton I.B.M. Mathematics Research Project, Princeton University, 1957, November 17 0085.35807 Google Scholar5 T. S. Motzkin, , H. Raiffa, , G. L. Thompson and , R. M. Thrall, H. W. Kuhn and , A. W. Tucker, The double description methodContributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N. J., 1953, 51–73, paper no. 3. MR0060202 0050.14201 CrossrefGoogle Scholar6 A. W. Tucker, Condensed Schemata for Dantzig's Simplex Method, Mimeographed, Princeton University, 1958, January Google Scholar7 A. W. Tucker, Linear inequalities and convex polyhedral sets, Proceedings of the Second Symposium in Linear Programming, Washington, D. C., 1955, National Bureau of Standards, Washington, D. C., 1955, 569–602, January 27-29 MR0075618 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Thermodynamic Tree: The Space of Admissible Paths11 February 2013 | SIAM Journal on Applied Dynamical Systems, Vol. 12, No. 1AbstractPDF (724 KB)Enumeration of All Extreme Equilibria of Bimatrix Games25 July 2006 | SIAM Journal on Scientific Computing, Vol. 23, No. 1AbstractPDF (221 KB)Methods for Global Concave Minimization: A Bibliographic Survey17 February 2012 | SIAM Review, Vol. 28, No. 3AbstractPDF (1828 KB)Generating All the Faces of a Polyhedron12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 26, No. 3AbstractPDF (1094 KB)Markov Renewal Programming by Linear Fractional Programming1 August 2006 | SIAM Journal on Applied Mathematics, Vol. 14, No. 6AbstractPDF (1321 KB)Programming Under Uncertainty: The Solution Set13 July 2006 | SIAM Journal on Applied Mathematics, Vol. 14, No. 5AbstractPDF (753 KB)Equilibrium Points of Bimatrix Games13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 4AbstractPDF (301 KB) Volume 9, Issue 1| 1961Journal of the Society for Industrial and Applied Mathematics History Submitted:15 June 1960Published online:10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0109008Article page range:pp. 72-88ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics