Sensitivity analysis for constraint and variational systems by means of set-valued differentiation

Abstract

In this paper we study general classes of parametric systems arising in optimization and related problems. We provide a local sensitivity analysis of such systems using tools of the generalized differentiation for nonsmooth and set-valued mappings. The main attention is paid to computing the so-called coderivatives of multi-valued solution maps and studying on this basis some concepts of robust Lipschitzian stability. The latter means that we ensure Lipschitzian properties of solution maps which are robust with respect to perturbations of the initial data. In this way, we obtain effective sufficient conditions as well as necessary and sufficient conditions for robust Lipschitzian stability with the evaluation of corresponding Lipschitz moduli.