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The Farkas Lemma revisited

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Abstract

Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.

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References

  1. Kjeldsen T. H., “Different motivations and goals in the historical development of the theory of systems of linear inequalities,“ Arch. Hist. Exact Sci., 56, No. 6, 459–538 (2002).

    Article  MathSciNet  Google Scholar 

  2. Floudas C. A. and Pardalos P. M. (eds.), Encyclopedia of Optimization, Springer-Verlag, Berlin and New York (2009).

    MATH  Google Scholar 

  3. Kusraev A. G. and Kutateladze S. S., Introduction to Boolean Valued Analysis [in Russian], Nauka, Moscow (2005).

    Google Scholar 

  4. Kusraev A. G. and Kutateladze S. S., Subdifferential Calculus: Theory and Applications. [in Russian], Nauka, Moscow (2007).

    Google Scholar 

  5. Bartl D., “A short algebraic proof of the Farkas lemma,“ SIAM J. Optim., 19, No. 1, 234–239 (2008).

    Article  MathSciNet  Google Scholar 

  6. Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities, Birkhäuser, Basel etc. (2009).

    MATH  Google Scholar 

  7. Downey L., “Farkas’ lemma and multilinear forms,“ Missouri J. Math. Sci., 21, No. 1, 65–67 (2009).

    MATH  MathSciNet  Google Scholar 

  8. Aron R., Downey L., and Maestre M., “Zero sets and linear dependence of multilinear forms,“ Note Mat., 25, No. 1, 49–54 (2005/2006).

    MathSciNet  Google Scholar 

  9. Jeyakumar V. and Li G.I., “Farkas’ lemma for separable sublinear functionals,“ Optim. Letters, 3, No. 4, 537–545 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  10. Fiedler M. et al., Linear Optimization Problems with Inexact Data, Springer-Verlag, New York (2006).

    MATH  Google Scholar 

  11. Mangasarian O. L., “Set containment characterization,“ J. Global Optim., 24, No. 4, 473–480 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  12. Giannessi F., Constrained Optimization and Image Space Analysis. Vol. 1: Separation of Sets and Optimality Conditions, Springer-Verlag, New York (2005).

    MATH  Google Scholar 

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Correspondence to S. S. Kutateladze.

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Original Russian Text Copyright © 2010 Kutateladze S. S.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 1, pp. 98–109, January–February, 2010.

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Kutateladze, S.S. The Farkas Lemma revisited. Sib Math J 51, 78–87 (2010). https://doi.org/10.1007/s11202-010-0010-y

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  • DOI: https://doi.org/10.1007/s11202-010-0010-y

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