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Farkas's Lemma

The Inequality $\left\langle{f_0, x}\right\rangle{}\leq 0$ follows from

\begin{displaymath}
\left\langle{f_1, x}\right\rangle{}\leq 0, \ldots, \left\langle{f_n, x}\right\rangle{}\leq 0
\end{displaymath}

Iff there exist Nonnegative numbers $\lambda_1$, ..., $\lambda_n$ with

\begin{displaymath}
\sum_{k=1}^n \lambda_k f_k=f_0.
\end{displaymath}

This Lemma is used in the proof of the Kuhn-Tucker Theorem.

See also Kuhn-Tucker Theorem, Lagrange Multiplier




© 1996-9 Eric W. Weisstein
1999-05-26