An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming
2005-11-07
Research Paper
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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
Automatically Extracted Terms
- problem
- condition
- proof
- kkt conditions
- fj conditions
- lemma
- nonlinear programming
- minimizer
- programming
- 1 i q
- vector
- mf constraint qualification
- l l 0
- function
- nonlinear
- constraint
- result
- optimization problem
- lemma 2.3
- lemma 2.1
