本文選題：向量平衡問題 + 向量變分不等式問題　； 參考：《廣西師范大學(xué)》2017年碩士論文

【摘要】：向量平衡問題是非線性泛函分析中重要的分支,在交通運(yùn)輸、金融工程、人力資源等領(lǐng)域有廣泛的應(yīng)用.本文主要研究?jī)深悊栴}:向量平衡問題和向量變分不等式問題解集的穩(wěn)定性.本論文總共分為四章,具體內(nèi)容如下:第一章,介紹向量平衡問題和向量變分不等式問題解集穩(wěn)定性的歷史背景和研究現(xiàn)狀,同時(shí)介紹本文要用到的一些常用符號(hào)、基本概念和引理.第二章,在自反Banach空間中研究向量平衡問題解集的弱上半連續(xù)性.首先,當(dāng)約束集和映射同時(shí)被不同的參數(shù)擾動(dòng)時(shí),利用向量平衡問題的間隙函數(shù)將向量平衡問題轉(zhuǎn)化為凸優(yōu)化問題,證明向量平衡問題解集的弱上半連續(xù)性.其次,我們將混合向量變分不等式問題轉(zhuǎn)化為平衡問題,利用向量平衡問題解集的穩(wěn)定性結(jié)果得到混合向量變分不等式解集的穩(wěn)定性.第三章,在自反Banach空間中研究向量變分不等式解集的穩(wěn)定性.當(dāng)約束集和映射同時(shí)被不同的參數(shù)擾動(dòng)時(shí),分別研究當(dāng)J-goF和F為緊上半連續(xù)映射時(shí),向量變分不等式解集的弱上半連續(xù)性、閉性.第四章,在Rn空間中,在約束集和映射同時(shí)被不同參數(shù)擾動(dòng)時(shí),利用向量變分不等式的拓?fù)涠?得到向量變分不等式解集的下半連續(xù)性.與已經(jīng)獲得的結(jié)果相比,我們不需要映射滿足任何單調(diào)性或者嚴(yán)格單調(diào)性條件,同時(shí),也不需要任何緊性條件.
[Abstract]:Vector balance problem is an important branch of nonlinear functional analysis, which is widely used in transportation, financial engineering, human resources and other fields. In this paper, we study the stability of solution sets for two kinds of problems: vector equilibrium problem and vector variational inequality problem. This paper is divided into four chapters. The main contents are as follows: the first chapter introduces the historical background and research status of the stability of vector equilibrium problem and vector variational inequality problem, and introduces some commonly used symbols in this paper. Basic concepts and Lemma. In chapter 2, we study the weak upper semicontinuity of solutions for vector equilibrium problems in reflexive Banach spaces. Firstly, when the constraint set and the mapping are disturbed by different parameters simultaneously, the vector equilibrium problem is transformed into a convex optimization problem by using the gap function of the vector equilibrium problem, and the weak upper semi-continuity of the solution set of the vector equilibrium problem is proved. Secondly, we transform the mixed vector variational inequality problem into a equilibrium problem, and obtain the stability of the solution set of mixed vector variational inequality by using the stability result of the solution set of vector equilibrium problem. In chapter 3, we study the stability of the solution set of vector variational inequalities in reflexive Banach spaces. When the constrained set and the mapping are disturbed by different parameters at the same time, the weak upper semicontinuity and closeness of the solution set of vector variational inequalities are studied respectively when J-goF and F are compact upper semicontinuous mappings. In chapter 4, when the constrained set and mapping are disturbed by different parameters at the same time in rn space, the lower half continuity of the solution set of vector variational inequality is obtained by using the topological degree of vector variational inequality. Compared with the obtained results, we do not need the mapping to satisfy any monotonicity or strict monotonicity condition, nor any compactness condition.
【學(xué)位授予單位】：廣西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O224

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前4條

1 敬燕;向量平衡問題解集的非空有界性[D];廣西師范大學(xué);2015年

2 左佳斌;自反Banach空間中非單調(diào)變分不等式解集的穩(wěn)定性分析[D];廣西師范大學(xué);2014年

3 陽(yáng)強(qiáng);向量變分不等式和向量?jī)?yōu)化問題解集的穩(wěn)定性研究[D];廣西師范大學(xué);2012年

4 鐘仁佑;變分不等式解集的穩(wěn)定性及連通性[D];廣西師范大學(xué);2008年

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本文編號(hào)：1799056