A convex, finite and lower semicontinuous function with empty subdifferential

We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal counterexample to various statements in convex analysis in which comple...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Author: Wachsmuth, Gerd
Format: Article
Language:English
Online Access:Get full text
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Summary:We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal counterexample to various statements in convex analysis in which completeness is required.
ISSN:2331-8422