The Constrained Gradient Method of Linear Programming

Next article The Constrained Gradient Method of Linear ProgrammingC. E. LemkeC. E. Lemkehttps://doi.org/10.1137/0109001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. M. L. Beale, On minimizing a convex function subject to linear inequalities, J. Roy. Statist. Soc. Ser. B., 17 (1955), 173–184; discussion, 194–203 MR0089101 0068.13701 Google Scholar[2] E. M. L. Beale, An alternative method for linear programming, Proc. Cambridge Philos. Soc., 50 (1954), 512–523 MR0063635 0056.13705 CrossrefGoogle Scholar[3] Garrett Birkhoff and , Saunders Mac Lane, A survey of modern algebra, Macmillan Co., New York, N. Y., 1953xi+472 MR0054551 0052.25402 Google Scholar[4] A. Charnes and , C. E. Lemke, Computational problems of linear programming, Proceedings of the Association for Computing Machinery, Pittsburgh, 1952, Richard Rimbach Associates, Pittsburgh, P. A., 1952, 97–98 MR0058308 Google Scholar[5] A. Cooper, W. W. Charnes and , M. Miller, Dyadic programs and sub-dual methods, Purdue Univ. Res. Proj. for Methodological Aspects of Management Science, 1957 Google Scholar[6] 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, Chap. XXI MR0056260 0045.09802 Google Scholar[7] G. B. Dantzig, , L. R. Ford, Jr. and , D. R. Fulkerson, W. H. Kuhn and , A. W. Tucker, A primal-dual algorithm for linear programsLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 171–181, paper no. 7 MR0089774 Google Scholar[8] David Gale, , Harold W. Kuhn and , Albert W. Tucker, C. T. Koopmans, Linear programming and the theory of gamesActivity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons Inc., New York, N. Y., 1951, 317–329 MR0046018 0045.09709 Google Scholar[9] H. W. And Tucker, A. W. Kuhn, Non-Linear Programming, Proceedings of the 2nd Berkeley Symposium on Mathematical Statististics and Probability, Univ. of Calif Press, Los Angeles, 1950 Google Scholar[10] C. E. Lemke, The dual method of solving the linear programming problem, Naval Res. Logist. Quart., 1 (1954), 36–47 MR0067582 0128.39605 CrossrefGoogle Scholar[11] J. K. Thurber, A Geometric Algorithm for Solving the General Linear Programming Problem, ONR Report IMM-NYU 249, New York University Institute of Mathematical Sciences, New York, 1958 Google Scholar[12] G. Zoutendijk, Maximizing a function in a convex region, J. Roy. Statist. Soc. Ser. B, 21 (1959), 338–355 MR0122578 0091.16101 Google Scholar Next article FiguresRelatedReferencesCited byDetails Extension of Davidon’s Variable Metric Method to Maximization Under Linear Inequality and Equality ConstraintsDonald Goldfarb12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 17, No. 4AbstractPDF (2500 KB) Volume 9, Issue 1| 1961Journal of the Society for Industrial and Applied Mathematics History Submitted:13 November 1959Published online:10 July 2006 InformationCopyright © 1961 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0109001Article page range:pp. 1-17ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics