The Subdiierential of the Optimal Solution in Parametric Optimization

If a strong suucient optimality condition of second order together with the Mangasarian-Fromowitz and the constant rank constraint quali-cations are satissed for a parametric optimization problem, then a local optimal solution is strongly stable in the sense of Kojima and the corresponding optimal solution function is locally Lipschitz continuous. In the article the possibilities for the computation of sub-gradients of this function are discussed. We will give formulae for the guaranteed computation of the entire subdiierential, provided that an additional assumption is satissed. An example will show the necessity of this assumption. Moreover, this assumption is diicult to be veri-ed. Without it, a subgradient can be computed with non-polynomial complexity in the worst case. A last approach yields a subgradient with probability one in polynomial time.