Nonlinear Cone Separation Theorems in Real Topological Linear Spaces

authored by

Christian Günther, Bahareh Khazayel, Christiane Tammer

Abstract

The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, and optimization. In the paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone/conical surface in real (topological) linear spaces. Basically, we follow the separation approach by Kasimbeyli [SIAM J. Optim., 20 (2010), pp. 1591-1619] based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Classical separation theorems for convex sets are the key tool for proving our main nonlinear cone separation theorems.

Organisation(s)

Institute of Applied Mathematics

External Organisation(s)

Martin Luther University Halle-Wittenberg

Type

Article

Journal

SIAM journal on optimization

Volume

34

Pages

225 - 250

No. of pages

26

ISSN

1052-6234

Publication date

03.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Software, Theoretical Computer Science, Applied Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2212.06293 (Access: Open)
https://doi.org/10.1137/22M1542003 (Access: Closed)