Work

On a Non-Prox-Regularity Example by Rockafellar and Wets

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.23279

Authors: Jasper, Isaac, Wang, Xianfu

Institutions: University of British Columbia, University of British Columbia, Okanagan Campus

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Universities Space Research Association, Natural Sciences and Engineering Research Council of Canada

OpenAlex ID: W7214034354

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