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Duality in Convex Programming and in Projective Space

1963; Society for Industrial and Applied Mathematics; Volume: 11; Issue: 3 Linguagem: Inglês

10.1137/0111039

2168-3484

Frank W. Sinden,

Optimization and Search Problems

Previous article Next article Duality in Convex Programming and in Projective SpaceFrank W. SindenFrank W. Sindenhttps://doi.org/10.1137/0111039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Herbert Busemann and , Paul J. Kelly, Projective geometry and projective metrics, Academic Press Inc., New York, N. Y., 1953viii+332 MR0054980 0052.37305 Google Scholar[2] H. S. M. Coxeter, The Real Projective Plane, McGraw-Hill Book Company, Inc., New York, N. Y., 1949x+196 MR0030205 0032.11302 Google Scholar[3] R. Courant and , D. Hilbert, Mathematische Physik II, Springer, Berlin, 1937 Google Scholar[4] Jack B. Dennis, Mathematical programming and electrical networks, The Technology Press of The Massachusetts Institute of Technology, Cambridge, Mass., 1959vi+186 MR0108400 Google Scholar[5] R. J. Duffin, Dual programs and minimum cost, J. Soc. Indust. Appl. Math., 10 (1962), 119–123 10.1137/0110011 MR0137588 0106.13905 LinkISIGoogle Scholar[6] David Gale, The theory of linear economic models, McGraw-Hill Book Co., Inc., New York, 1960xxi+330 MR0115801 Google Scholar[7] W. S. Dorn, A duality theorem for convex programs, IBM J. Res. Develop, 4 (1960), 407–413 MR0114672 0095.14503 CrossrefISIGoogle Scholar[8] F. W. Sinden, A geometric representation for pairs of dual quadratic or linear programs, J. Math. Anal. Appl., 5 (1962), 378–402 10.1016/0022-247X(62)90014-8 MR0145997 CrossrefGoogle Scholar[9] W. Fenchel, Convex Cones, Sets and Functions, mimeographed notes of lectures, Princeton, 1953 Google Scholar[10] E. Steinitz, Bedingt convergente Reihen and konvexe Systems III, Journ. Reine Angew. Math., 146 (1916), 1–52 Google Scholar[11] Kenneth J. Arrow and , Alain C. Enthoven, Quasi-concave programming, Econometrica, 29 (1961), 779–800 MR0138509 0104.14302 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 11, Issue 3| 1963Journal of the Society for Industrial and Applied Mathematics History Submitted:15 June 1962Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111039Article page range:pp. 535-552ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics