このエントリーをはてなブックマークに追加
ID 41503
FullText URL
Title Alternative
Nonlinear Generalizations of Tucker's Theorem on Inequality Systems
Author
Fujimoto, Takao
Ishiyama, Ken-ichi
Abstract
This note is to prove Tucker's theorem on linear inequalities based on the proof method of minimax theorems which uses Kakutani's fixed point theorem. One device is necessary to convert the minimax theorems to Tucker's formulation. This is a slight restriction on the image sets when creating a set-valued map. We also present nonlinear generalizations of Tucker's theorem employing the same method. All we need is that the set of variable values for which an objective function attains its maximum is convex. This objective function is a convex combination of functions. We also present a proof of the fact that a local characterization of inequality systems, when a given mapping is differentiable, can be made global provided the mapping is concave.
Note
研究ノート (Note)
Published Date
1999-12-10
Publication Title
岡山大学経済学会雑誌
Publication Title Alternative
Okayama Economic Review
Volume
volume31
Issue
issue3
Publisher
岡山大学経済学会
Publisher Alternative
The Economic Association of Okayama University
Start Page
163
End Page
171
ISSN
0386-3069
NCID
AN00032897
Content Type
Journal Article
language
日本語
File Version
publisher
Refereed
True
Eprints Journal Name
oer