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Stability Analysis of Solution Sets for Vector Variational Inequalities and Vector Optimization Problems

Author: YangQiang
Tutor: ZhongRenYou; FanJiangHua
School: Guangxi Normal University
Course: Basic mathematics
Keywords: Vector variational inequality Set-valued mixed weak variational inequality Vector optimization problem Aubin Property Leray-Schauder fixed point theorem Topologicaldegree theory Stability Lower semicontinuity
CLC: O178
Type: Master's thesis
Year: 2012
Downloads: 25
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Abstract


In this thesis, we study the stability of solutions sets for parametric set-valued mixed weak vector variational inequalities and parametric vector optimization problems. This thesis is divided into three chapters.In chapter1, we briefly introduce the current research of vector variational inequality and vector Optimization problems. In addition, we introduce some basic notations and preliminaries.In chapter2, we study the stability of solution sets for vector variational inequalities in finite dimensional spaces. We obtain the lower semicontinuity of the solution mapping for the parametric set-valued mixed weak vector variational inequality with strictly C-f pseudomono-tone mapping. Moreover, under some requirements that the mapping satisfies Leray-Schauder conditions, we obtain some existence theorems for parametric set-valued mixed weak vector vari-ational inequality. Finally, we establish the lower semicontinuity of the solution mapping for the parametric set-valued mixed weak vector variational inequality, by using the degree-theoretic approach.In chapter3, we study the stability of solution sets for vector optimization problem in finite dimensional spaces. We obtain the lower semicontinuity of the solution mapping for the parametric set-valued vector optimization problem with stricfly C-convex mapping. Moreover, under some requirements that the mapping satisfies Leray-Schauder conditions, we obtain some existence theorems for parametric set-valued vector optimization. Finally, under some different conditions, we establish the lower semicontinuity of the solution mapping for parametric single-valued vector optimization problem, by using the degree-theoretic approach.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Inequality and other
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