An elementary proof of the Karush–Kuhn–Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints
Olga Brezhneva, Alexey A Tret’yakov · Optimization · 2010
We present an elementary proof of the Karush–Kuhn–Tucker theorem for the problem with a finite number of nonlinear inequality constraints in normed linear spaces under the linear independence constraint qualification. Most proofs in the literature rely on advanced concepts and results such as the convex separation theorem and Farkas, lemma. By contrast, the proofs given in this article, including a proof of the lemma, employ only basic results from linear algebra. The lemma derived in this article represents an independent theoretical result.