一种新的向量互补问题

本文在实局部凸空间中引入了一种新的向量互补问题，这一向量互补问题不仅包含了由Ｙｕ和Ｙａｏ提出的广义向量互补问题由Ｃｈｅｎ和Ｙａｎｇ定义的弱向量互补问题，而且还包含了Ｉｓａｃ意义下的隐互补问题。本文还讨论了新的向量互补问题，向量变分不等式，向量单向极小化问题和最小元问题之间的关系，给出了这一向量互补问题解的存在定理。

A NEW KIND OF VECTOR COMPLEMENTARITY PROBLEM

In this paper,a new kind of vector complementarity problem is introduced. This vector complementarity problem includes not only the generalized vector complementarity problem prosposed by Yu Yao and the weak vector complementarity problem definited by Chen Yang,but also the implicit complementarity problem in the sense of Isac. The relation among the new kind of vector complementarity problem, the vector variational inequality, the vector unilateral minimization problem and the minimal element problem are also discussed in this paper.The existence theorems of solutions for this vector complementarity problem are given.