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For the Karush-Kuhn Tucker optimsation problem, Wikipedia notes that:

"The necessary conditions are sufficient for optimality if the objective function f and the inequality constraints g_j are continuously differentiable convex functions and the equality constraints h_i are affine functions." link

Could someone please show me how this result is derived? That is, given a convex objective function, convex inequality constraints and affine equality constraints, how can we show that any point in the feasible set that satisfies the KKT conditions must be a minimizer of the function over the feasible set?

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