The directional subdifferential of the difference of two convex functions

Authors:
Jean-Paul Penot
Affiliations:
Faculté des Sciences, Mathématiques UMR CNRS 5142, PAU Cedex, France 64013
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

We provide a criterion giving a formula for the directional (or contingent) subdifferential of the difference of two convex functions. We even extend it to the difference of two approximately starshaped functions. Our analysis relies on a notion of approximate monotonicity for operators which is much less demanding than the usual one.