The Karush–Kuhn–Tucker (KKT) Conditions
This is a set of necessary conditions, which a local minimizer θ* of the problem given in (C.29) has to satisfy. If θ* is a point that satisfies the regularity condition, then there exists a vector λ of Lagrange multipliers so that the following
are valid:(C.30)
Actually, there is a fourth condition concerning the Hessian of the Lagrangian function, which is not of interest to us. The
above set of equations is also part of the sufficiency conditions; however, in this case, there are a few subtle points and
the interested reader is referred to more specialized textbooks, for example, [Baza 79, Flet 87,
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