Nonlinear Opt.: KKT- theorem 1

Introduction

The Karush-Kuhn-Tucker theorem (short: KKT-Theorem) is a way of nonlinear optimization. It is based on Lagrange optimization. Beside the additional conditions of the Lagrange attempt there are some other extra conditions which are called KKT-conditions. The aim of this theory is to solve a problem with additional conditions in form of inequaliities.

The first mention of the KKT-conditions was in the master thesis of William Karush in 1939. But it became more famous in 1951 where Harold W. Kuhn and Albert W. Tucker presented it in a conference paper.

KKT-Conditions

In the following chapter the conditions will be demonstrated in a mathematical form:

(1) Fehler beim Parsen (http://mathoid.testme.wmflabs.org Serverantwort ist ungültiges JSON.): \frac{\delta L}{\delta x_{j}}= \frac{\delta f}{\delta x_{j}}\left ( \widehat{x} \right )+ \sum_{i=1}^{m} \widehat{\lambda_{i}}\cdot \frac{\delta g_{i}}{\delta x_{j}}\left ( \widehat{x} \right )\geq 0