摘要
研究一般凸集约束下自反Banach空间极大单调集值映射变分不等式的解的存在性,首先利用集值映射锐角原理,提出了一个例外簇的概念,由此给出变分不等式问题解存在的一个充分条件.对于伪单调变分不等式问题,它是解存在的充要条件.把文献[1]变分不等式问题解的存在性推广到自反Banach空间极大单调集值映射.
The existence of the solutions of the variational inequality problem with a maximal monotone set-valued map on a reflexive a Banach space under a general convex constrained set is discussed in this paper. A concept exceptional family for the problem by using acute angle principle of set-valued map is proposed. Based on this concept, a sufficient condition for the existence of the solution of the variational inequality problem is given. Also that this condition is both necessary and sufficient to pseudomonotone variational inequalities problem, is confivmed.
出处
《北京建筑工程学院学报》
2006年第4期77-79,共3页
Journal of Beijing Institute of Civil Engineering and Architecture
关键词
自反BANACH空间
集值映射
极大单调
例外簇
变分不等式
reflexive Banach space
set-valued map
maximal monotone
exceptional family
variational inequality
