Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 601-623 |
| Seitenumfang | 23 |
| Fachzeitschrift | Journal of Nonlinear and Variational Analysis |
| Jahrgang | 8 |
| Ausgabenummer | 4 |
| Frühes Online-Datum | 1 Mai 2024 |
| Publikationsstatus | Veröffentlicht - 1 Aug. 2024 |
Abstract
In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by Garcia-Castaño, Melguizo-Padial and Parzanese.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Journal of Nonlinear and Variational Analysis, Jahrgang 8, Nr. 4, 01.08.2024, S. 601-623.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Nonlinear strict cone separation theorems in real normed spaces
AU - Günther, Christian
AU - Tammer, Christiane
AU - Khazayel, Bahareh
N1 - Publisher Copyright: © 2024 Journal of Nonlinear and Variational Analysis.
PY - 2024/8/1
Y1 - 2024/8/1
N2 - In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by Garcia-Castaño, Melguizo-Padial and Parzanese.
AB - In this paper, we derive some new results for the separation of two not necessarily convex cones by a (convex) cone / conical surface in real (reflexive) normed spaces. In essence, we follow the nonlinear and nonsymmetric separation approach developed by Kasimbeyli (2010, SIAM J. Optim. 20), which is based on augmented dual cones and Bishop-Phelps type (normlinear) separating functions. Compared to Kasimbeyli's separation theorem, we formulate our theorems for the separation of two cones under weaker conditions (concerning convexity and closedness requirements) with respect to the involved cones. By a new characterization of the algebraic interior of augmented dual cones in real normed spaces, we are able to establish relationships between our cone separation results and the results derived by Kasimbeyli (2010, SIAM J. Optim. 20) and by Garcia-Castaño, Melguizo-Padial and Parzanese.
KW - Augmented dual cone
KW - Bishop-Phelps cone
KW - Cone separation
KW - Nonconvex cone
KW - Separation theorem
UR - http://www.scopus.com/inward/record.url?scp=85193048832&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2303.06392
DO - 10.48550/arXiv.2303.06392
M3 - Article
VL - 8
SP - 601
EP - 623
JO - Journal of Nonlinear and Variational Analysis
JF - Journal of Nonlinear and Variational Analysis
SN - 2560-6921
IS - 4
ER -