Dually cone-boundedness of a set and applications
Optimization and Control
2026-01-13 v1 Functional Analysis
Abstract
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the cone. We show that this is a weaker notion when compared to other similar ones and we explore several links with the existing literature. We subsequently demonstrate that this concept furnishes the properties required to obtain various generalizations of important results and techniques, including conic cancellation rules and the R{\aa}dstr\"om embedding procedure.
Cite
@article{arxiv.2601.07517,
title = {Dually cone-boundedness of a set and applications},
author = {Marius Durea and Elena-Cristina Stamate},
journal= {arXiv preprint arXiv:2601.07517},
year = {2026}
}