| | | | | 一种新的向量互补问题 | | | 殷洪友,徐成贤 | | | 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以及由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．
【作者单位】：西安交通大学理学院!西安710049
【关键词】：向量互补问题;向量变分不等式;等价性;存在定理
【分类号】：O177
【DOI】：cnki:ISSN:0255-7797.0.1999-04-012
【正文快照】：
１ 引言最近，Ｙｕ和Ｙａｏ在实Ｂａｎａｃｈ空间中提出了广义向量互补问题的概念［１］，这一向量互补问题也是Ｃｈｅｎ和Ｙａｎｇ所定义的弱向量互补问题的推广［２］．由于向量互补问题在向量优化、最优控制理论和经济学等多个领域中具有重要应用，关于这一问题的研究日益受到重视．本文将在实局部凸空间中引入一种新的向量互补问题，此类互补问题不仅包含了上述两种向量互补问题，而且还包含了Ｉｓａｃ意义下的隐互补问题［３］．本文也将讨论新的向量互补问题、向量变分不等式、向量单向极小化问题（在弱有效点的意义下）和最小元问题… | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | A NEW KIND OF VECTOR COMPLEMENTARITY PROBLEM | | | Yin Hongyou(殷洪友) Xu Chengxian(徐成贤) (School of Science;Xian Jiaotong University;Xian 710049) | | | 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.
【Keyword】：vector complementarity problems;vector variational inequalities;equivalence;existence theorems |
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