研究生: |
林清炎 Ching-Yan Lin |
---|---|
論文名稱: |
變異型態的變分不等式 Variant Problems On Variational Inequalilties |
指導教授: |
朱亮儒
Chu, Liang-Ju |
學位類別: |
博士 Doctor |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2002 |
畢業學年度: | 90 |
語文別: | 英文 |
論文頁數: | 91 |
中文關鍵詞: | 一致點定理,最大最小不等式, 、固定點定理. |
英文關鍵詞: | Coincidence theorem, minimax ine-, quality, Nikaido's coincidence theor-, em,Gorniewicz fixed point theorem,, nearly convex, G-space , Bregman -, type proximal point algorithm. |
論文種類: | 學術論文 |
相關次數: | 點閱:229 下載:5 |
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In this paper, we establish existence theory and algorithms on
variational problems, by which we mean here problems of fixed
points, coincidences, minimax inequalities, generalized variat-
ional inequalities, generalized quasi-variational inequalities.
Under weakened assumptions on the operators and constraint reg-
ions, we improve and generalize recently many well-known exist-
ence theorems. More specifically, we establish two versions of
Nikaidos coincidence theorem from different approaches, and use
these to show several existence theorems for the generalized v-ariational inequalities, in the case that C is noncompact and
nonconvex, but merely a nearly convex set. Also, we introduce
a new Bregman-type proximal point algorithm for solving variat-
ional inequalitiy problems in a reflexive Banach space, and pr-
ovide a continuation method to solve nonsmooth convex programm-
ing.
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