Formulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.

Keywords:

subdifferential regularity, directional regularity, directionally Lipschitzian functions subdifferential regularity, directional regularity, directionally Lipschitzian functions

MSC Classifications:

49J52, 58C20, 49J50, 90C26 show english descriptions Nonsmooth analysis [See also 46G05, 58C50, 90C56]
Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]
Frechet and Gateaux differentiability [See also 46G05, 58C20]
Nonconvex programming, global optimization 49J52 - Nonsmooth analysis [See also 46G05, 58C50, 90C56]
58C20 - Differentiation theory (Gateaux, Frechet, etc.) [See also 26Exx, 46G05]
49J50 - Frechet and Gateaux differentiability [See also 46G05, 58C20]
90C26 - Nonconvex programming, global optimization

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