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. EI 2005-43). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from http://hdl.handle.net/1765/7030
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