Conjugation-Based Approach to the $\varepsilon $-Subdifferential of Convex Suprema

Author:

Correa Rafael,Hantoute Abderrahim,López Marco A.

Abstract

AbstractWe provide new characterizations of the $\varepsilon $ ε -subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.

Funder

Research Project from MICINN, Spain

MICIU of Spain and Universidad de Alicante

AICO of Generalitat Valenciana

Basal CMM

Australian ARC - Discovery Projects

Law Offices of Anidjar and Levine, P.A.

Universidad de Alicante

Publisher

Springer Science and Business Media LLC

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