變異型態的變分不等式

Variant Problems On Variational Inequalilties

林清炎(Ching-Yan Lin)

指導教授 ： 朱亮儒

國立臺灣師範大學/理學院/數學系/博士(2001年)

摘要

無

關鍵字

一致點定理,最大最小不等式, ； 固定點定理. ； HASH(0xb5f6f18) ； HASH(0xb5f6f90) ； HASH(0xb5f7008)

並列摘要

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.

並列關鍵字

Coincidence theorem, minimax ine- ； quality, Nikaido's coincidence theor- ； em,Gorniewicz fixed point theorem, ； nearly convex, G-space , Bregman - ； type proximal point algorithm.