An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming
12 Pages Posted: 26 Aug 2006
Date Written: 14 2005, 10
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
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