New Tour on the Subdifferential of Supremum via Finite Sums and Suprema

This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our fo...

Full description

Saved in:
Bibliographic Details
Published in:Journal of optimization theory and applications 2022-06, Vol.193 (1-3), p.81-106
Main Authors: Hantoute, A., López-Cerdá, M. A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Banach spaces
Calculus of Variations and Optimal Control
Optimization
Convex analysis
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Sums
Theory of Computation
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01925-9