On Global Error Bounds for Convex Inequalities Systems

Vo Si Trong Long ()
Additional contact information
Vo Si Trong Long: University of Science

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 15, 1359-1384

Abstract: Abstract In this paper, we first present necessary and sufficient conditions for the existence of global error bounds for a convex function without additional conditions on the function or the solution set. In particular, we obtain characterizations of such global error bounds in Euclidean spaces, which are often simple to check. Second, we prove that under a suitable assumption the subdifferential of the supremum function of an arbitrary family of convex continuous functions coincides with the convex hull of the subdifferentials of functions corresponding to the active indices at given points. As applications, we study the existence of global error bounds for infinite systems of linear and convex inequalities. Several examples are provided as well to explain the advantages of our results with existing ones in the literature.

Keywords: Convex inequality; Global error bounds; Infinite systems of convex inequalities; The PLV property; Uncertain linear inequality systems; 90C25; 90C34; 90C05; 49J52 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02458-7 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:202:y:2024:i:3:d:10.1007_s10957-024-02458-7

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

DOI: 10.1007/s10957-024-02458-7

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 ().