# Kuhn-Tucker conditions

### From Glossary

Abbreviated KT and KKT (latter credits Karush, who had the conditions in his earlier thesis).

This is the Lagrange Multiplier Rule, which Kuhn and Tucker published as an extension to allow inequality constraints. They also introduced the notion of a constraint qualification (which had been only the linear independence condition stemming from Lagrange's multiplier theorem). The most important contribution that sets KT apart from similar discoveries is the connection with saddle points that led to Lagrangian duality.