Hilbert空间中一类新广义非线性变分不等式组问题  

A New Class of Generalized Nonlinear Variational Inequalities Problem in Hilbert Space

作　　者：罗静[1] 隆建军[2] 

机构地区：[1]四川理工学院理学院,四川自贡643000 [2]攀枝花市大河中学,四川攀枝花617061

出　　处：《四川理工学院学报（自然科学版）》2015年第4期80-85,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

摘　　要：变分不等式原理是当今数学技术中一个有力的研究工具,有重要的学术研究价值和意义。在运筹学、计算机科学、系统科学、工程技术、交通和经济与管理等方面有着广泛而重要的应用。利用η-次微分算子的预解算子技巧和辅助原理技术,研究Hilbert空间中的一类广义非线性变分不等式组问题,得出该问题的解。在此基础上,引入一个带有Lipschitz连续、强单调和松弛单调映射的辅助性问题,并且利用预解算子和集值压缩映像的不动点定理证明了解的存在性与唯一性,这一结果推广、改进和发展了相关文献的结果。Variational inequality principle is a powerful research tool in the current mathematical technology,and has important academic research value and significance. It is widely and importantly applied in operations research,computer science,system science,engineering technology,transportation,economic and management and other aspects. In this essay,by using the resolvent operator technique and the auxiliary principle technique of η a differential operator,a class of generalized nonlinear variational inequalities problem in Hilbert space is researched,and the solution of the problem is obtained. On this basis,a auxiliary problem with Lipschitz continuous,strongly monotone and relaxed monotone mapping is introduced,and the existence and the uniqueness of the solution are proved by using the resolvent operator and the fixed point theorem of set-valued contractive mappings. This result has extended,improved and developed the results in relevant literatures.

关 键 词：广义非线性变分不等式组 预解式技术 辅助原理技术 迭代算法 收敛性 

分 类 号：O177.1[理学—数学]