Quasidifferntiability of optimal solutions in parametric optimal solutions in parametric nonlinear optimization
Stephan Dempe, Diethard Pallaschke · Optimization · 1997
Let x o be a locally optimal Solution of a Smooth Parametric nonlinear optimizattion problem min: for a fixed value v – v o if the strong sufficient optimalily condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint qualitications are satistied. then v o is strongly stable In the sense of Kojima and the corresponding function of locally optimal solutions 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 quasidifferentiable in the sense of Dem'yanov and Rubinov and deseribe one quasidifferential.In the last part of the paper a method is developed for reducing the quasidifferential which is especially useful when both the super- and the subdifferential are spanned by finitely many elements as in our case.