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

Ş.İ. Birbil, J.B.G. Frenk, G.J. Still

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)479-484
Number of pages6
JournalEuropean journal of operational research
Volume180
Issue number1
DOIs
Publication statusPublished - 1 Jul 2007

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