非凸限制區域上的向量值擬變分不等式

Generalized Vector Quasi-Variational Inequalities On Nonconvex Constraint Regions

吳采燕(Tsai-Yen Wu)

指導教授 ： 朱亮儒

國立臺灣師範大學/理學院/數學系/碩士(2000年)

摘要

這論文的要旨有兩層:
(1)我們利用一般化的KKM mapping 概念,首先得到廣義的 G´orniewicz固定點定理;
(2)藉著應用我們的固定點定理,建立幾個廣義的向量值擬變分不等式(GVQVI)的存在性定理.我們在既不是凸的亦不是緊緻的,而僅僅只是在 nearly convex 的區域上推論出幾個結果.

關鍵字

近似凸集 ； 非環函數 ； 擬Q函數 ； KKM函數 ； 一般向量值擬變分不等式 ； 極大向量值擬變分不等式

並列摘要

We introduce a new class of nonconvex sets, which are named nearly convex set, and then extend several existence results on nonconvex optimization problems. In fact, the purpose of this paper is two fold: (1) we first obtain a rather general version of the G´orniewicz fixed point theorem by using the concept of generalized KKM mappings; (2) we establish some existence theorems for generalized vector quasi-variational inequality problems by applying our fixed point theorem. We derive several results here neither convex nor compact on constraint

並列關鍵字

nearly convex ； acyclic multifunction ； Q-quasiconvex ； KKM mapping ； generalized vector quasi-variational inequality ； maximal vector quasi-variational inequality

參考文獻

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