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For a constrained optimization problem, in general the KKT conditions are a necessary but not sufficient condition for a point to be the local maxima/minima of the objective function.

Is it always true that if the point is not a local maxima/minima, it must be a saddle point of the objective function?

For simplicity, we can assume that all functions involved are differentiable at least once. But I don't want to make any assumptions about second derivative or convexity.

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    Math@SE is a better choice of venue for this question.2011-11-30

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