An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming
Ş. İlker Birbil, Hans Frenk, Georg J. Still · EUR Research Repository (Erasmus University Rotterdam) · 2005
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.