Nonsmoothness and quasidifferentiability

On reduced pairs of bounded closed convex sets

“…It should be mentioned that the space K(X)/ ∼ , K(X) = {A ∈ B(X) | A is compact}, plays important role in quasidifferential calculus [2].…”

On quasidifferential kernels

“…A function defined in R n , f, is said to be uniformly directionally differentiable at xeR n if for any e>0 there exists an <* 0 >0 such that |f (x+ad)-f (x)-f' (x;ad) |<ae, Vae(0,a 0 ], VdcB^O), [13], [4,Ch. 3].…”

“…(1.1) f'(x;d) = p (d)-p_(d) = max <v,d> -max <w,d>, ve3f (x) we-af(x) where both of p^d) and p 2 (d) are sublinear operators, i.e., as the sum form of a pair of sublinear operator and superlinear operator, or as the difference form of two sublinear operators, [4], [8], [13]. This kind of structure of derivatives of quasidifferentiable function brings on that a quasidifferential of a quasidifferentiable function, called bidifferential also in [7], is not unique, but the quasidifferential class of equivalence of a quasidifferentiable function is unique.…”

Decomposition of Minkowski–Rådström–Hörmander Space to the Direct Sum of Symmetric and Asymmetric Subspaces

“…The relation of MRH space to B(X) can be compared to the relation of the ring Z of integers to the semigroup of natural numbers N. A MRH space appears very useful in a theory of generalized differentiation developed by many authors (see for example Rockafellar and Wets [22] and Mordukhovich [14]). A MRH space is closely related to quasidifferential calculus of Demyanov and Rubinov [1,2]. In particular the structure of a vector space enables differentiation of multifunctions (see for example [6]).…”