本文選題：廣義集值向量似變分不等式　切入點(diǎn)：廣義強(qiáng)向量擬均衡問(wèn)題組　出處：《渤海大學(xué)》2017年碩士論文

【摘要】：變分不等式屬均衡優(yōu)化問(wèn)題,在國(guó)民經(jīng)濟(jì)的諸多領(lǐng)域有重要應(yīng)用.向量變分不等式、向量均衡問(wèn)題是變分不等式的推廣形式,其解的存在性研究是變分不等領(lǐng)域的研究熱點(diǎn)問(wèn)題,受到許多學(xué)者的特別關(guān)注.而誤差界是研究變分不等式解映射穩(wěn)定性和靈敏度分析的前提,間隙函數(shù)是獲得變分不等式解的誤差界的一個(gè)有效的辦法.因此對(duì)幾類變分不等式問(wèn)題解的存在性和誤差界的研究具有重要的理論意義和應(yīng)用價(jià)值.本論文主要研究了廣義集值向量似變分不等式、廣義強(qiáng)向量擬均衡問(wèn)題組解的存在性以及廣義混合擬變分不等式的間隙函數(shù)和全局誤差界.本論文所取得的主要結(jié)果概括如下:第二章主要考慮Banach空間中兩類廣義集值向量似變分不等式問(wèn)題.利用KKM定理,在集合的緊性和凸性條件下,并利用集值映射的下半連續(xù)性和映射的仿射性條件得到了兩類廣義集值向量似變分不等式解的存在性結(jié)果.第三章利用集值映射的自然擬C-凸性和集值映射的下(-C)-連續(xù)性的定義和Glicksberg-Fan-Kakutani不動(dòng)點(diǎn)定理,在不要求錐C的對(duì)偶錐C*具有弱*緊基的情況下,建立了集值廣義強(qiáng)向量擬均衡問(wèn)題組解的存在性定理.第四章在Hilbert空間中引入了一類新的廣義混合擬變分不等式利用引入的正則間隙函數(shù)和D-間隙函數(shù),在所涉及映射的強(qiáng)混合單調(diào)性和Lipschitz連續(xù)性等條件下,得到了廣義混合擬變分不等式的全局誤差界結(jié)果.
[Abstract]:Variational inequalities are equilibrium optimization problems and have important applications in many fields of national economy.Vector variational inequalities and vector equilibrium problems are the generalization of variational inequalities. The existence of their solutions is a hot issue in the field of variational inequality, which has been paid special attention to by many scholars.The error bound is the premise to study the mapping stability and sensitivity analysis of variational inequality solution. The gap function is an effective method to obtain the error bound of variational inequality solution.Therefore, the study on the existence of solutions and error bounds for some variational inequality problems has important theoretical significance and application value.In this paper, we study the existence of solutions for generalized set-valued vector-like variational inequalities, generalized strong vector quasi-equilibrium problems, and the gap functions and global error bounds of generalized mixed quasi-variational inequalities.The main results obtained in this paper are summarized as follows: in chapter 2, we consider two classes of generalized set-valued vector variational-like inequalities in Banach spaces.By using KKM theorem, under the conditions of compactness and convexity of sets, and by using the lower semicontinuity of set-valued mappings and affine conditions of mappings, the existence of solutions of two classes of generalized set-valued vector variational-like inequalities is obtained.In chapter 3, by using the definition of natural quasi C convexity of set-valued mappings and the lower Ca-continuity of set-valued mappings and the Glicksberg-Fan-Kakutani fixed point theorem, the dual cone C * of cone C is not required to have a weak * compact basis.The existence theorems of solutions for set-valued generalized strong vector quasi equilibrium problems are established.In chapter 4, we introduce a new class of generalized mixed quasi-variational inequalities in Hilbert spaces under the conditions of strong mixed monotonicity and Lipschitz continuity of the mappings, using the regular gap function and the D-gap function.The global error bounds for generalized mixed quasi-variational inequalities are obtained.
【學(xué)位授予單位】：渤海大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O178

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