The Kuhn-Tucker conditions are a set of mathematical criteria used in optimization problems, particularly in constrained optimization. They help determine the optimal solution when there are constraints on the variables. These conditions extend the Lagrange multiplier method, allowing for inequality constraints in addition to equality constraints. In essence, the Kuhn-Tucker conditions provide necessary conditions for a solution to be optimal. They involve the original objective function, the constraints, and the associated multipliers. By satisfying these conditions, one can identify points that may represent local maxima or minima in the presence of constraints.