The Karush–Kuhn–Tucker (KKT) conditions are a set of necessary conditions for a solution to be optimal for a constrained optimization problem. They are widely used in mathematical optimization, particularly in nonlinear programming. The KKT conditions generalize the method of Lagrange multipliers to handle problems with inequality constraints.
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For differentiable inequality constraints , a regular local minimum has multipliers satisfyingFor a convex problem under a suitable constraint qualification, these conditions are sufficient for global optimality.