It is intended, in this work, to present the Kuhn-Tucker theorem with the consideration of infinite inequalities. So the mathematical fundaments of this result, not so important in Mathematical Programming but a very challenging problem from the mathematical point of view, are presented in a very simple way. It is shown how this result can be obtained in the context of real Hilbert spaces using the separation theorems.

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Hilbert spaces,Separation theorems,Kuhn-Tucker’s theorem,Infinite inequalities dimension