This is Thomas Lehmann's talk "What is ... the Kuhn-Tucker theorem?" at the "What is ...?" seminar. The talk was given on Friday, April 29, 2011, 12:00pm at the BMS Loft at Urania.
The Kuhn-Tucker theorem is the foundation of nonlinear programming. Requiring a constraint qualification, it states necessary conditions for local solutions of nonlinear programs. Even more, these (Karush-)Kuhn-Tucker conditions are the basis of many efficient nonlinear programming algorithms.
For more "What is ...?" seminar videos, visit math.fu-berlin.de/w/Math/WhatIsSeminar.