Nonlinear Cone Separation Theorems in Real Topological Linear Spaces

verfasst von

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

Martin-Luther-Universität Halle-Wittenberg

Typ

Artikel

Journal

SIAM journal on optimization

Band

34

Seiten

225 - 250

Anzahl der Seiten

26

ISSN

1052-6234

Publikationsdatum

03.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Software, Theoretische Informatik, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2212.06293 (Zugang: Offen)
https://doi.org/10.1137/22M1542003 (Zugang: Geschlossen)