On second-order subdifferentials and their applications

We study second-order subdifferentials of nonsmooth functions that are particularly important for applications to sensitivity analysis in optimization and related problems. First we develop various calculus rules for these subdifferentials in rather general settings. Then we obtain exact formulas for computing the second-order subdifferentials for a class of separable piecewise smooth functions. Functions of this class arise, in particular, in equilibrium models related to some practical problems of continuum mechanics. Finally we provide applications of the obtained results to Lipschitzian stability of parametric variational and hemivariational inequalities and efficiently express the derived conditions in terms of the initial data for selected problems of continuum mechanics.