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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.

    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,phi) 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,phi) 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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