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 MultiplierExplore with Wolfram|Alpha
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 TheoremCite this as:
Weisstein, Eric W. "Kuhn-Tucker Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kuhn-TuckerTheorem.html