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General Inequalities 4 pp 365–367Cite as

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An Application of Farkas’ Lemma to a Nonconvex Minimization Problem

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Abstract

A duality theory is developed for a certain type of quasiconvex minimization problem making use of Farkas’ Lemma for systems of linear (convex) inequalities.

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References

  1. M. Avriel, W.E. Diewert, S. Schaible and W.T. Ziemba, Introduction to concave and generalized concave functions. In: S. Schaible and W.T. Ziemba (eds.), Generalized concavity in optimization and economics, Academic Press, New York, 1981, 21–50.

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  2. J.P. Crouzeix, A duality framework in quasiconvex programming. In: S. Schaible and W.T. Ziemba (eds.), Generalized concavity in optimization and economics. Academic Press, New York, 1981, 207–225.

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  3. J.P. Crouzeix, J.A. Ferland and S. Schaible, Duality in generalized linear fractional programming. Math. Programming 27 (1983) (to appear).

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  4. J. Farkas, Über die Theorie der einfachen Ungleichungen. J. Reine Angew. Math. 124 1902), 1–24.

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  5. R. Jagannathan and S. Schaible, Duality in generalized fractional programming via Farkas’ Lemma. J. Optim. Theory Appl. 41 1983), 417–424.

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  6. R.T. Rockafellar, Convex Analysis. Princeton 1970.

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Author information

Authors and Affiliations

  1. Department of Management Science, University of Iowa, Iowa City, IA, 55240, USA

    Raj Jagannathan

  2. Department of Finance and Management Science, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Siegfried Schaible

Authors
  1. Raj Jagannathan
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  2. Siegfried Schaible
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Editor information

Editors and Affiliations

  1. Mathematisches Institut I, Universität Karlsruhe, Kaiserstrasse 12, D-7500, Karlsruhe 1, Germany

    Wolfgang Walter

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© 1984 Springer Basel AG

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Jagannathan, R., Schaible, S. (1984). An Application of Farkas’ Lemma to a Nonconvex Minimization Problem. In: Walter, W. (eds) General Inequalities 4. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6259-2_35

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  • DOI: https://doi.org/10.1007/978-3-0348-6259-2_35

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6261-5

  • Online ISBN: 978-3-0348-6259-2

  • eBook Packages: Springer Book Archive

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