Symmetric and Non-Symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: García-Castaño, Fernando, Günther, Christian, Melguizo-Padial, M. A., Tammer, Christiane
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909777664147456
author García-Castaño, Fernando
Günther, Christian
Melguizo-Padial, M. A.
Tammer, Christiane
author_facet García-Castaño, Fernando
Günther, Christian
Melguizo-Padial, M. A.
Tammer, Christiane
contents In this paper, we study relationships between symmetric and non-symmetric separation of (not necessarily convex) cones by using separating cones of Bishop-Phelps type in real normed spaces. Besides extending some known results for the non-symmetric cone separation approach, we propose a new symmetric cone separation approach and establish cone separation results for it by using some cone separation results obtained for the non-symmetric cone separation approach twice (by swapping the roles of the cones). In addition to specifically emphasizing the results for the convex case, we also present some existence results for (bounded) convex bases of convex cones. Finally, we highlight some applications of symmetric and non-symmetric cone separation in optimization.
format Preprint
id arxiv_https___arxiv_org_abs_2503_10184
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Symmetric and Non-Symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces
García-Castaño, Fernando
Günther, Christian
Melguizo-Padial, M. A.
Tammer, Christiane
Optimization and Control
90C29, 90C25, 90C31, 90C48, 46N10
In this paper, we study relationships between symmetric and non-symmetric separation of (not necessarily convex) cones by using separating cones of Bishop-Phelps type in real normed spaces. Besides extending some known results for the non-symmetric cone separation approach, we propose a new symmetric cone separation approach and establish cone separation results for it by using some cone separation results obtained for the non-symmetric cone separation approach twice (by swapping the roles of the cones). In addition to specifically emphasizing the results for the convex case, we also present some existence results for (bounded) convex bases of convex cones. Finally, we highlight some applications of symmetric and non-symmetric cone separation in optimization.
title Symmetric and Non-Symmetric Cone Separation via Bishop-Phelps Cones in Normed Spaces
topic Optimization and Control
90C29, 90C25, 90C31, 90C48, 46N10
url https://arxiv.org/abs/2503.10184