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.
|Keywords||Fritz-John conditions, Karush-Kuhn-Tucker conditions, nonlinear programming|
Birbil, S.I., Frenk, J.B.G., & Still, G.J.. (2005). An Elementary Proof of the Fritz-John and Karush-Kuhn-Tucker Conditions in Nonlinear Programming (No. ERS-2005-057-LIS). ERIM report series research in management Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/6992