Suppose you have a local minimizer x of a function f(x). Knowing that x is a local minimizer, can you say it is a Kuhn Tucker point?
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Generally Kuhn Tucker only appears when you have some form of constraint. Did you mean to ask something else? It would be a Kuhn Tucker point, but only in a vacuous sense, since $\nabla f(x) = 0$. – copper.hat Oct 27 '15 at 17:47
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Suppose you have a constraint g(x) <= 0, and the point satisfies the constraint as well. Is it then necessarily a Kuhn Tucker point? – ThinkConnect Oct 27 '15 at 17:49
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No. Take $g(x) = (x-2)^2$ and $f(x) = x$, then you cannot write $\nabla f(2) + \lambda \nabla g(2) = 0$ for any $\lambda$. You need some regularity conditions so the multiplier of the cost gradient is non zero. – copper.hat Oct 27 '15 at 17:50