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Lemma 15.9 (Fritz John, corrected): at a constrained minimizer w⋆ there are multipliers α₀ ≥ 0, αᵢ ≥ 0, not all zero, vanishing off the active set, with α₀∇f(w⋆) + ∑ αᵢ∇gᵢ(w⋆) = 0 · Prove2Me