Maximal monotone relations and the second derivatives of nonsmooth functions (Q1067594)

In the nonsmooth analysis of \textit{F. H. Clarke} [Optimization and nonsmooth analysis (New York 1983)], a set-valued mapping \(\partial f\) is associated with an extended real-valued function f on \(R^ n\). The elements of \(\partial f(x)\) are called the generalized gradients of f at x. The author presents a number of facts that help to clarify some issues concerning the generalized second derivatives of nonsmooth functions. Namely, it is shown that the Clarke tangent cone at any point of a maximal monotone relation is a linear subspace.