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Nonlinear separation methods and applications for vector equilibrium problems using improvement sets.
- Source :
-
Applicable Analysis . Nov2021, Vol. 100 Issue 15, p3182-3198. 17p. - Publication Year :
- 2021
-
Abstract
- In this paper, the image space analysis is applied to investigate a vector equilibrium problem using improvement sets and with matrix inequality constraints. First, a nonlinear scalar regular weak separation function is constructed by using the oriented distance function and the norm function. Then, a global saddle-point condition for a generalized Lagrange function is investigated. It is shown that the existence of a saddle point is equivalent to a nonlinear separation of two suitable subsets in the image space. Furthermore, a gap function and an error bound are obtained in terms of the nonlinear scalar regular weak separation function under suitable assumptions. As applications, an optimality condition, a gap function and an error bound for a strategic game with vector payoffs are also given. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ERROR functions
*STRATEGY games
*EQUILIBRIUM
*MATRIX inequalities
Subjects
Details
- Language :
- English
- ISSN :
- 00036811
- Volume :
- 100
- Issue :
- 15
- Database :
- Academic Search Index
- Journal :
- Applicable Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 152741722
- Full Text :
- https://doi.org/10.1080/00036811.2020.1712372