Integrability of subdifferentials of directionally Lipschitz functions

Integrability of Subdifferentials of Directionally Lipschitz Functions

Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.

^-representation of Subdifferentials of Directionally Lipschitz Functions

Subdifferentials of convex functions and some regular functions f are expressed in terms of limiting gradients at points in a given dense subset of dorn Vf.

On Directionally Dependent Subdifferentials

In this paper directionally contextual concepts of variational analysis, based on dual-~pace cou-siructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulnes~, necessary and ft!so sufficient optimality conditions in terms of directioual subdiffeJ • ent.ials are established , and it is shown that they can be effective in the situations where known opti...

Rotund Norms, Clarke Subdifferentials and Extensions of Lipschitz Functions

Lipschitz functions with maximal Clarke subdifferentials are staunch

In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.