Quasidiierentiability of Optimal Solutions in Parametric Nonlinear Optimization

Let x 0 be a locally optimal solution of a smooth parametric nonlinear optimization problem minff(x; y) : g(x; y) 0; h(x; y) = 0g for a xed value y = y 0. If the strong suucient optimality condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint qualiications are satissed, then x 0 is strongly stable in the sense of Kojima and the corresponding function of locally optimal solutions of perturbed problems is locally Lipschitz continuous. In the paper we give one tool for computing its generalized Jacobian. We also show that this function is quasidiierentiable in the sense of Dem'yanov and Rubinov and describe one quasidiierential. In the last part of the paper a method is developed for reducing the quasidiierential which is especially useful when both the super-and the subdiierential are spanned by nitely many elements as in our case.