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

12 Pages Posted: 26 Aug 2006

See all articles by S. Ilker Birbil

S. Ilker Birbil

J. B. G. Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ; Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

G. Still

University of Twente - Department of Applied Mathematics

Date Written: 14 2005, 10

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.

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

JEL Classification: M, L15, O32, C61

Suggested Citation

Birbil, S. Ilker and Frenk, J.B.G. (Hans) and Still, G., An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming (14 2005, 10). ERIM Report Series Reference No. ERS-2005-057-LIS. Available at SSRN: https://ssrn.com/abstract=828179

J.B.G. (Hans) Frenk

Erasmus University, Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 0 10 408 1257 (Phone)
+31 0 10 408 9162 (Fax)

Erasmus University, Rotterdam (EUR) - Erasmus Research Institute of Management (ERIM)

P.O. Box 1738
3000 DR Rotterdam
Netherlands

G. Still

University of Twente - Department of Applied Mathematics ( email )

P.O. Box 217
7500 AE Enschede
Netherlands
+31 53 489 3404 (Phone)
+31 53 489 4858 (Fax)

HOME PAGE: http://wwwhome.math.utwente.nl/~stillgj/

No contact information is available for S. Ilker Birbil

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