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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
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.
新潟大学
1990
eng
journal article
http://hdl.handle.net/10191/5658
https://niigata-u.repo.nii.ac.jp/records/2193
AA10800960
13419951
Nihonkai Mathematical Journal
Nihonkai Mathematical Journal
1
2
209
227
https://niigata-u.repo.nii.ac.jp/record/2193/files/5_0003.pdf
application/pdf
2.7 MB
2019-07-29