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An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming

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  • Birbil, S.I.
  • Frenk, J.B.G.
  • Still, G.J.
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    Abstract

    In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets.

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    File URL: http://hdl.handle.net/1765/6992
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    Bibliographic Info

    Paper provided by Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam. in its series Research Paper with number ERS-2005-057-LIS.

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    Date of creation: 14 Oct 2005
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    Handle: RePEc:dgr:eureri:30007658

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    Web page: http://www.erim.eur.nl/

    Related research

    Keywords: Fritz-John conditions; Karush-Kuhn-Tucker conditions; nonlinear programming;

    This paper has been announced in the following NEP Reports:

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