On the regularity of the Kuhn-Tucker curve

We consider twice continuously differentiable finite dimensional optimization problems, depending on a real parameter. Besides a discussion of (local) Lipschitz continuity of the Kuhn-Tucker curve, we present conditions under which the Kuhn-Tucker curve is piecewise continuously differentiable. Throughout the paper we assume the linear independence of the gradients of the binding constraint functions. We use Kojima's concept of strongly stable Kuhn-Tucker points and present a new equivalent formulation of this concept.