Details
| Original language | English |
|---|---|
| Pages (from-to) | 225 - 250 |
| Number of pages | 26 |
| Journal | SIAM journal on optimization |
| Volume | 34 |
| Issue number | 1 |
| Early online date | 16 Jan 2024 |
| Publication status | Published - Mar 2024 |
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.
Keywords
- augmented dual cone, base, Bishop-Phelps cone, cone separation, nonconvex cone, seminorm, separation theorem
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Applied Mathematics
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In: SIAM journal on optimization, Vol. 34, No. 1, 03.2024, p. 225 - 250.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Nonlinear Cone Separation Theorems in Real Topological Linear Spaces
AU - Günther, Christian
AU - Khazayel, Bahareh
AU - Tammer, Christiane
N1 - Publisher Copyright: © 2024 Society for Industrial and Applied Mathematics.
PY - 2024/3
Y1 - 2024/3
N2 - 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.
AB - 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.
KW - augmented dual cone
KW - base
KW - Bishop-Phelps cone
KW - cone separation
KW - nonconvex cone
KW - seminorm
KW - separation theorem
UR - http://www.scopus.com/inward/record.url?scp=85190170226&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2212.06293
DO - 10.48550/arXiv.2212.06293
M3 - Article
VL - 34
SP - 225
EP - 250
JO - SIAM journal on optimization
JF - SIAM journal on optimization
SN - 1052-6234
IS - 1
ER -