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Symmetric Duality for Continuous Linear Programs

Published: 01 January 1970 Publication History
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  • Abstract

    A strong duality theorem for continuous linear programs is established and a two-level maximal principle derived as a consequence. The method of proof is constructive, indicating that optimal solutions of approximating linear programs converge to the optimal solution of the continuous problem.

    References

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    William F. Tyndall, A duality theorem for a class of continuous linear programming problems, J. Soc. Indust. Appl. Math., 13 (1965), 644–666
    [2]
    William F. Tyndall, An extended duality theorem for continuous linear programming problems, SIAM J. Appl. Math., 15 (1967), 1294–1298
    [3]
    N. Levinson, A class of continuous linear programming problems, J. Math. Anal. Appl., 16 (1966), 73–83
    [4]
    David Gale, The theory of linear economic models, McGraw-Hill Book Co., Inc., New York, 1960xxi+330
    [5]
    A. J. Goldman, H. W. Kuhn, A. W. Tucker, Resolution and separation theorems for polyhedral convex setsLinear inequalities and related systems, Annals of Mathematics Studies, no. 38, Princeton University Press, Princeton, N. J., 1956, 41–51
    [6]
    R. Grinold, Masters Thesis, Continuous programming, Doctoral thesis, University of California, Berkeley, 1968
    [7]
    Richard Bellman, Dynamic programming, Princeton Univeristy Press, Princeton, N. J., 1957xxv+342
    [8]
    Richard E. Bellman, Stuart E. Dreyfus, Applied dynamic programming, Princeton University Press, Princeton, N.J., 1962xxii+363

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    Published In

    cover image SIAM Journal on Applied Mathematics
    SIAM Journal on Applied Mathematics  Volume 18, Issue 1
    Jan 1970
    257 pages
    ISSN:0036-1399
    DOI:10.1137/smjmap.1970.18.issue-1
    Issue’s Table of Contents

    Publisher

    Society for Industrial and Applied Mathematics

    United States

    Publication History

    Published: 01 January 1970

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