An elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions in nonlinear programming

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Birbil, Ş.İ. and Frenk, J.B.G. and Still, G.J. (2007) An elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions in nonlinear programming. European Journal of Operational Research, 180 (1). pp. 479-484. ISSN 0377-2217

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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.

Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/61926
Official URL:http://dx.doi.org/10.1016/j.ejor.2006.04.012
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Metis ID: 241919