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

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. (c) 2006 Elsevier B.V. All rights reserved.