摘要
证明了在无限维的Banach空间中,当假设映射是紧场和伪单调时,变分不等式的解集非空有界等价于它的严格可行性,将文献(Facchinei F,Pang J S.Finite-dimensional Variational Inequalities and ComplementarityProblems[M].NewYork:Springer-Verlag,2003.)中定理2.4.4从有限维欧氏空间推广到了无限维的Banach空间.
In this paper, it is proved that, in Bananch spaces of possibly infinite dimentions, the solution set of variational inequality problem VIP（ K, F） being nonempty and bounded is equivalent to its strict feasibility, provided the mapping F is compact field and pseudo-monotone in the sense of Karamardian. This generalizes some known results from finite dimensional spaces to infinite dimensional spaces.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2009年第4期424-426,共3页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(10701059)
四川省青年科学基金(06ZQ026-013)资助项目
关键词
广义投影映射
变分不等式
拓扑度
紧场
伪单调映射
Generalized projection operator
Variational inequality
Topological degree
Compact field
Pseudo-monotone mapping
