A convex, finite and lower semicontinuous function with empty subdifferential
Optimization and Control
2024-09-30 v1
Abstract
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.
Cite
@article{arxiv.2409.18650,
title = {A convex, finite and lower semicontinuous function with empty subdifferential},
author = {Gerd Wachsmuth},
journal= {arXiv preprint arXiv:2409.18650},
year = {2024}
}