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研究生:林清炎
研究生(外文):Ching-Yan Lin
論文名稱:變異型態的變分不等式
論文名稱(外文):Variant Problems On Variational Inequalilties
指導教授:朱亮儒朱亮儒引用關係
指導教授(外文):Liang-Ju Chu
學位類別:博士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
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:91
中文關鍵詞:一致點定理最大最小不等式固定點定理.
外文關鍵詞:Coincidence theoremminimax ine-qualityNikaido''''s coincidence theor-emGorniewicz fixed point theoremnearly convexG-spaceBregman -type proximal point algorithm.
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  • 被引用被引用:0
  • 點閱點閱:124
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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.
Chapter 1. Introduction 1
Chapter 2. Extension of Nikaido''s Coincidence Theorem
2.1 Definitions and Preliminaries 5
2.2 Two Versions of Nikaido''s Coincidence Theorem 12
2.3 Applications to GVI(T,C, hi) 20
Chapter 3. Minimax and Quasi-variational Inequalities in G-paces
3.1 Definitions and Preliminaries 31
3.2 Main Results 36
3.3 Applications to GQVI(S,T,X, hi) 45
Chapter 4. A New Proximal Point Algorithm for Variational Inequalities
4.1 Definitions and Preliminaries 49
4.2 Convergence Analysis of BPPA 59
4.3 Convergence Property under Some Variant Monotonicity 64
Chapter 5. An Approach to Solving Convex Programmings with Nonsmoo?
th Objectives
5.1 Definitions and Preliminaries 71
5.2 Existence and Continuity 74
5.3 Maximality and Uniqueness of Optimal Solutions 78
Reference 85
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