Coderivative Calculus and Robust Lipschitzian Stability of Variational Systems

The paper deals with a broad class of parametric variational systems in infinite-dimensional spaces and mainly concerns their robust Lipschitzian stability with respect to parameter perturbations. We develop a local sensitivity analysis for such systems based on advanced tools of generalized differentiation. A special attention is paid to variational systems arising as solution maps to variational inequalities, problems of parametric optimization, and their extensions. A number of the results obtained are new even in finite-dimensional settings.