The basic aim of so-called quasidifferentiable analysis is to extend the classical differential calculus to special classes of nonsmooth functions. Such classes are, for example, continuous convex functions, or, more generally, locally Lipschitz functions. In the case of convex functions it is so-called convex analysis (cf. for instance, Rockafellar (1970)). In the case of Lipschitz functions the essential step in this direction was given by Clarke, who developed so-called nonsmooth analysis (see Clarke (1975), (1983)). However, the approach proposed by Clarke has a certain disadvantage. Namely, we make correspond to a given function f(x) at every point x a convex set ∂f| x of linear functionals. In other words, we have a point-to-set valued mapping which does not satisfy the classical Leibniz formula for products.
KeywordsOpen Subset Convex Function Lipschitz Function Directional Derivative Commutative Algebra
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