@article{oai:niigata-u.repo.nii.ac.jp:00002193,
author = {Tanaka, Tamaki},
issue = {2},
journal = {Nihonkai Mathematical Journal, Nihonkai Mathematical Journal},
month = {},
note = {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.},
pages = {209--227},
title = {A Characterization of Generalized Saddle Points for Vector-Valued Functions via Scalarization},
volume = {1},
year = {1990}
}