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1.
Qamrul Hasan Ansari Siegfried Schaible Jen-Chih Yao 《Journal of Global Optimization》2002,22(1-4):3-16
In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions. 相似文献
2.
In this paper, we investigate vector complementarity problems with a variable ordering relation. We establish existence results of a solution of a vector complementarity problem under an inclusive type condition. We obtain equivalence results among a vector complementarity problem, a vector variational inequality problem and other related problems. 相似文献
3.
研究了一类集值映象的广义向量变分不等式和相补问题 ,证明了解的一些存在性定理 .推广和改进了文 [1 ,4 6 ]的相关研究成果 . 相似文献
4.
In this paper, two vector implicit variational inequalities and three vector implicit complementarity problems are introduced
with a more general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions.
Furthermore, some existence theorems of the vector implicit variational inequalities are proved. We answered the open question
proposed by Rapcsák [Nonconvex Optim., Appl., Vol. 38, Kluwer Acad. Publ., Dordrecht, 2000, pp. 371–380].
This work was supported by the National Natural Science Foundation of China and the Scientific Research Foundation for the
Returned Overseas Chinese, Scholars, State Education Ministry. 相似文献
5.
The purpose of this paper is to discuss the feasibility and solvability of vector complementarity problems. We prove that, under suitable conditions, the vector complementarity problem with a pseudomonotonicity assumption is solvable whenever it is strictly feasible. By strengthening the generalized monotonicity condition, we show also that the homogeneous vector complementarity problem is solvable whenever it is feasible. At last, we study the solvability of the vector complementarity problem on product spaces.The authors thank Professor Franco Giannessi for valuable comments and suggestions leading to improvements of this paper. 相似文献
6.
本文引入了几类向量F-互补问题并给出了向量F-互补问题与广义向量变分不等式之间的关系.通过定义向量F-互补问题的可行集,研究了伪单调型向量F-互补问题的可行集的最小问题,推广了已有的一些结果. 相似文献
7.
In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex
cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational
inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems
is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones
depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of
vector complementarity problems, vector variational inequalities, and minimal element problems are also given.
While this paper was being revised in September 2006, Professor Alex Rubinov (the second author of the paper) left us due
to the illness. This is a very sad news to us. We dedicate this paper to the memory of Professor Rubinov as a mathematician
and truly friend. 相似文献
8.
本文利用纯量化方法及KKM技巧,研究向量变分和向量拟变分不等式解的存在性问题,作为应用本文还研究了向量互补问题及最优化问题解的存在性及其等价性刻划。本文结果改进和推广了已有的结果。 相似文献
9.
The natural quasi-concavity of set-valued mappings in an ordered vector space is introduced. Existence theorems for vector equilibrium problems involving set-valued monotone mappings are obtained and the convexity of the solution set is shown. 相似文献