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Karush-Kuhn-Tucker conditions

For differentiable inequality constraints

g_{i} (x) \leq 0

, a regular local minimum has multipliers

λ_{i} \geq 0

satisfying

\nabla f + \sum_{i} λ_{i} \nabla g_{i} = 0, λ_{i} g_{i} = 0.

For a convex problem under a suitable constraint qualification, these conditions are sufficient for global optimality.

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