2024-04-17T14:33:43Z
https://niigata-u.repo.nii.ac.jp/oai
oai:niigata-u.repo.nii.ac.jp:00002193
2022-12-15T03:35:04Z
176:488:489
453:454
A Characterization of Generalized Saddle Points for Vector-Valued Functions via Scalarization
A Characterization of Generalized Saddle Points for Vector-Valued Functions via Scalarization
Tanaka, Tamaki
7425
vector optimization
scalarization
two-person game
cone saddle points
equilibrium points
convex-concave functions
In this paper, we propose abstract concepts of saddle points of a vector-valued function ƒ defined on a product X × Y of infinite-dimensional sets X and Y in locally convex topological vector spaces. Three notions of the generalized saddle points are considered, and a notions of semi-saddle points, which is also known as "Nash equilibrium points" for a two-person nonzero-sum game in game theory, is defined for a pair of scalarized functions. Various necessary conditions, sufficient conditions and existence conditions are explored for each type of the generalized saddle points. These conditions give a connection between each type of the generalized saddle points and the corresponding type of the semi-saddle points.
journal article
新潟大学
1990
application/pdf
Nihonkai Mathematical Journal
2
1
209
227
Nihonkai Mathematical Journal
AA10800960
13419951
https://niigata-u.repo.nii.ac.jp/record/2193/files/5_0003.pdf
eng