The Kuhn-Tucker theorem is a theorem in nonlinear programming which states that if a regularity condition holds and and the functions are convex, then a solution which satisfies the conditions for a vector of multipliers is a global minimum. The Kuhn-Tucker theorem is a generalization of Lagrange multipliers. Farkas's lemma is key in proving this theorem.

# Kuhn-Tucker Theorem

## See also

Farkas's Lemma, Lagrange Multiplier## References

Kampas, F. J. "Tricks of the Trade: Using Reduce to Solve the Kuhn-Tucker Equations."*Mathematica J.*

**9**, 686-689, 2005.

## Referenced on Wolfram|Alpha

Kuhn-Tucker Theorem## Cite this as:

Weisstein, Eric W. "Kuhn-Tucker Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Kuhn-TuckerTheorem.html