Convex Duality

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120sfoundation (3/10)state theorem

For a CONVEX problem min f (x) s.t. g_{i} (x) \leq 0, h_{j} (x) = 0 with strong duality (e.g., Slater holds), what are the KARUSH-KUHN-TUCKER (KKT) conditions at a primal-dual optimal (x^{*}, λ^{*}, ν^{*}) ?