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

Ilker Birbil, Hans Frenk and G.J. Still

ERIM Report Series Research in Management from 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

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: Fritz-John conditions; Karush-Kuhn-Tucker conditions; nonlinear programming (search for similar items in EconPapers)
JEL-codes: C61 L15 M O32 (search for similar items in EconPapers)
Date: 2005-10-14
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