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Again on the Farkas Theorem and the Tucker Key Theorem Proved Easily

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  • Giorgio Giorgi

    (Department of Economics and Management, University of Pavia)

Abstract

The purpose of this paper is twofold; first, to present a simple proof of the Farkas theorem (or Farkas lemma or Farkas-Minkowski lemma), proof performed through a nonlinear theorem of the alternative; second, to present various new proofs of the so-called "Tucker key theorem", and to show that these two results are essentially equivalent.

Suggested Citation

  • Giorgio Giorgi, 2014. "Again on the Farkas Theorem and the Tucker Key Theorem Proved Easily," DEM Working Papers Series 094, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:demwp0094
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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0094.pdf
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    References listed on IDEAS

    as
    1. J. B. G. Frenk & G. Kassay, 1999. "On Classes of Generalized Convex Functions, Gordan–Farkas Type Theorems, and Lagrangian Duality," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 315-343, August.
    2. Illés, T. & Kassay, G., 1994. "Farkas type theorems for generalized convexities," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 5(2), pages 225-239.
    3. De Giuli, M.E., Giorgi, G. & Magnani, U., 1997. "A general linear theorem of the alternative: how to get its special cases quickly," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 8(2-4), pages 215-232.
    4. Morishima, Michio, 1969. "Theory of Economic Growth," OUP Catalogue, Oxford University Press, number 9780198281641.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Farkas lemma; Farkas theorem of the alternative; Tucker key theorem; Gordan theoren; Stiemke theorem; Motzkin theorem;
    All these keywords.

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