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Multiple Criteria Decision Making pp 64–75Cite as

Existence and Duality in Multiple Objective Linear Programming

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 130))

Abstract

This paper presents some existence and duality properties of linear vector optimization problems. The respective theory comprises the existence and duality properties of linear programming as a special form of a more general theoretical framework.

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References

  1. Evans, J.P. and Steuer R.E., “A Revised Simplex Method for Linear Multiple Objective Programs”, Mathematical Programming, Vol. 5 (1973), pp. 54–72.

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  2. Gale, D., The Theory of Linear Economic Models, McGraw-Hill, New York, 1960.

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  3. Isermann, H., “Proper Efficiency and the Linear Vector Maximum Problem”, Operations Research, Vol. 22, (1974), pp. 189–19. 1.

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  4. Krek, B., Linear Programming, Sir Isaak Pitman & Sons, London, 1968.

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  5. Mangasarian, O.L., Nonlinear Programming, McGraw-Hill, New York, 1969.

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  6. Motzkin, T., Beiträge zur Theorie der linearen Ungleichungen, Azriel, Jerusalem, 1936.

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  7. Wolfe, P., “A Duality Theorem for Nonlinear Programming”, Quarterly of Applied Mathematics, Vol. 19, (1961), pp. 239–244.

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Author information

Authors and Affiliations

  1. University of Saarland, Germany

    Heinz Isermann

Authors
  1. Heinz Isermann
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Editor information

Editors and Affiliations

  1. Centre d’Enseignement Superieur des Affaires, Chambre de Commerce et d’Industrie de Paris, 78350, Jouy-en-Josas, France

    Hervé Thiriez

  2. School of Management, State University of New York at Buffalo, 14214, Buffalo, N. Y., USA

    Stanley Zionts

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© 1976 Springer-Verlag Berlin Heidelberg

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Isermann, H. (1976). Existence and Duality in Multiple Objective Linear Programming. In: Thiriez, H., Zionts, S. (eds) Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87563-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-87563-2_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07794-7

  • Online ISBN: 978-3-642-87563-2

  • eBook Packages: Springer Book Archive

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