Details
| Original language | English |
|---|---|
| Pages (from-to) | 481-498 |
| Number of pages | 18 |
| Journal | Journal of Nonlinear and Variational Analysis |
| Volume | 9 |
| Issue number | 4 |
| Publication status | Published - 1 Aug 2025 |
Abstract
This paper focuses on the investigation of regularity conditions by virtue of the image space analysis, based on nonconvex separation. We consider a scalar constrained optimization problem and employ the Gerstewitz separation function, which is well known from scalarization of vector optimization problems to present and investigate a collection of nonlinear weak separation functions in connection with methods of image space analysis. With the separation theorems associated with the Gerstewitz function, some image regularity conditions which guarantee the existence of a weak separation function, conducting a regular separation, are studied. In addition, a Lagrange type function and a penalty function are constructed, while the existence of saddle points and exact penalty functions are established by means of the image regularity conditions.
Keywords
- Exact penalty function, Gerstewitz function, Image space analysis, Nonlinear separation function, Regularity condition, Saddle point
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of Nonlinear and Variational Analysis, Vol. 9, No. 4, 01.08.2025, p. 481-498.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Image regularity conditions based on nonconvex separation with applications
AU - Yao, Chaoli
AU - Tammer, Christiane
AU - Günther, Christian
N1 - Publisher Copyright: ©2025 Journal of Nonlinear and Variational Analysis.
PY - 2025/8/1
Y1 - 2025/8/1
N2 - This paper focuses on the investigation of regularity conditions by virtue of the image space analysis, based on nonconvex separation. We consider a scalar constrained optimization problem and employ the Gerstewitz separation function, which is well known from scalarization of vector optimization problems to present and investigate a collection of nonlinear weak separation functions in connection with methods of image space analysis. With the separation theorems associated with the Gerstewitz function, some image regularity conditions which guarantee the existence of a weak separation function, conducting a regular separation, are studied. In addition, a Lagrange type function and a penalty function are constructed, while the existence of saddle points and exact penalty functions are established by means of the image regularity conditions.
AB - This paper focuses on the investigation of regularity conditions by virtue of the image space analysis, based on nonconvex separation. We consider a scalar constrained optimization problem and employ the Gerstewitz separation function, which is well known from scalarization of vector optimization problems to present and investigate a collection of nonlinear weak separation functions in connection with methods of image space analysis. With the separation theorems associated with the Gerstewitz function, some image regularity conditions which guarantee the existence of a weak separation function, conducting a regular separation, are studied. In addition, a Lagrange type function and a penalty function are constructed, while the existence of saddle points and exact penalty functions are established by means of the image regularity conditions.
KW - Exact penalty function
KW - Gerstewitz function
KW - Image space analysis
KW - Nonlinear separation function
KW - Regularity condition
KW - Saddle point
UR - http://www.scopus.com/inward/record.url?scp=105005267963&partnerID=8YFLogxK
U2 - 10.23952/jnva.9.2025.4.02
DO - 10.23952/jnva.9.2025.4.02
M3 - Article
VL - 9
SP - 481
EP - 498
JO - Journal of Nonlinear and Variational Analysis
JF - Journal of Nonlinear and Variational Analysis
SN - 2560-6921
IS - 4
ER -