PreprintCC BY 4.0arXiv
On a Non-Prox-Regularity Example by Rockafellar and Wets
Abstract
We analyze a counterexample concerning non-prox-regular functions provided by Rockafellar and Wets in their 1998 foundational monograph, \textit{Variational Analysis}. By establishing a general theorem on the continuity of set-valued mappings, we show that the counterexample does not have its intended properties. We propose a slight adjustment to the construction and prove that the corrected version serves as the desired counterexample.
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BibTeX
@misc{jasper2026nonproxregularity,
title = {{On a Non-Prox-Regularity Example by Rockafellar and Wets}},
author = {Isaac Jasper and Xianfu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23279},
eprint = {2609.23279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23279},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a Non-Prox-Regularity Example by Rockafellar and Wets
AU - Isaac Jasper
AU - Xianfu Wang
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23279
UR - https://arxiv.org/abs/2609.23279
AB - We analyze a counterexample concerning non-prox-regular functions provided by Rockafellar and Wets in their 1998 foundational monograph, \textit{Variational Analysis}. By establishing a general theorem on the continuity of set-valued mappings, we show that the counterexample does not have its intended properties. We propose a slight adjustment to the construction and prove that the corrected version serves as the desired counterexample.
ER -