A New Derivation of the Kuhn-Tucker Conditions

Abstract

The Kuhn-Tucker necessary conditions for a local maximum of a differentiable function subject to differentiable inequality constraints, are derived by showing that the classical necessary conditions for a local maximum of a differentiable function of N variables subject to less than N equality constraints, are also meaningful when there are N or more equality constraints, if appropriate assumptions, similar to Kuhn and Tucker's “constraint qualification,” are made.