Karush–Kuhn–Tucker conditions

In mathematical optimization, the Karush-Kuhn-Tucker (KKT) conditions are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear optimization to be optimal, provided that some regularity conditions are statisfied. 
Allowing inequality constraints, the KKT approach to nonlinear optimization generalizes the method of Lagrange multipliers, which allows only equality constraints.