Integral-Type Representations for the Subdifferential of Suprema

Rafael Correa () and Abderrahim Hantoute ()
Additional contact information
Rafael Correa: Universidad de Chile
Abderrahim Hantoute: Universidad de Alicante

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 22, 1659-1685

Abstract: Abstract An integral-like representation is provided for the $$\varepsilon $$ ε -subdifferential of the supremum of an arbitrary family of convex functions. Our characterizations are expressed through appropriate discrete sums performed on the data functions $$f_{t}$$ f t ’s together with specific singular measures operating on them. Moreover, as long as the underlying space is a reflexive Banach space or a separable normed space, we substitute these additional measures with related limits that involve the data functions. All the objects involved in our characterizations rely intrinsically on the data functions that are (almost) active at the reference point.

Keywords: Convex functions; $$\varepsilon $$ ε -subdifferential; Supremum function; 26B05; 26J25; 49H05 (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02545-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02545-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-024-02545-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().