Semismoothness and directional subconvexity of functions

Authors: Huỳnh Văn Ngãi, Jean-Paul Penot,

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Publisher, magazine: ,

Publication year: 2007

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Abstract

The relationships between the semismoothness of a function and the submonotonicity of its subdifferentials at some given point are studied. A notion of approximate starshapedness at that point is introduced and compared with these properties. Some criteria ensuring that different subdifferentials coincide at that point are obtained.

Tags: approximate convexity; nonsmooth analysis; semismoothness; starshaped function; subconvexity; subdifferential