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研究生:蔡玉玲
研究生(外文):Tsai, Yu Lin
論文名稱:鞍點及極大極小點存在定理之研究
論文名稱(外文):On Genenalized Vector Saddle Points and Generalized Vector Minimax Theorems for Set-Valued Maps and Vector Valued Functions
指導教授:林來居林來居引用關係
指導教授(外文):Lin, Lai Jiu
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:35
中文關鍵詞:鞍點極大極小定理變分不等式
外文關鍵詞:Saddle PointMinimax TheoremVariational inequality
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在這篇論文裡,我們首先證明多值映射或向量值函數的推廣向量鞍點存在定理,然後導出推廣向量極大極小值定理的存在定理。我們也可以建立向量值函數的推廣向量quasi- variational-like不等式問題的存在定理及推廣向量鞍點問題和推廣向量quasi- variational- like不等式問題;兩者間解的關係,由此我們又建立出另一個向量鞍點問題的存在定理。

In this paper, we first prove some existence theorems of generalized vector saddle point for multivalued map or vector valued function. As a consequence, we establish the existence theoremsof generalized vector minimax theorem. We also establish the existencetheorem of generalized vector quasi-variational-like inequality problem for vector valued function and the relationship between the solutions of the generalized vector saddle point problem and the generalized vectorquasi-variational-like inequality problem for vector valued functions.From which we establish another existence theorem of generalized vector saddle point problems.

1.Abstract and Introduction ………………… 1
2.Preliminaries ……………………………… 4
3.Generalized vector saddle point……………… 10
4.Generalized vector minimax theorems ……… 17
5.Generalized vector saddle point problem and
generalized vector quasi-variational-like
inequality problem …………………… 23
References …………………………………… 33

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