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

Ş.İ. Birbil; J.B.G. Frenk; G.J. Still

doi:10.1016/j.ejor.2006.04.012

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

Ş.İ. Birbil
, J.B.G. Frenk
, G.J. Still

Discrete Mathematics and Mathematical Programming

Research output: Contribution to journal › Article › Academic › peer-review

25 Citations (Scopus)

10 Downloads (Pure)

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.

Original language	English
Pages (from-to)	479-484
Number of pages	6
Journal	European journal of operational research
Volume	180
Issue number	1
DOIs	https://doi.org/10.1016/j.ejor.2006.04.012
Publication status	Published - 1 Jul 2007

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10.1016/j.ejor.2006.04.012

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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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AU - Still, G.J.

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AB - 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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DO - 10.1016/j.ejor.2006.04.012

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JF - European journal of operational research

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

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