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1引言设R~n.R_+n.R_+~n分别表示Euclidean空间及R~n的非负和正子空间:符号┃·┃表示向量或矩阵的2-范数,非线性互补问题(NLCP) 相似文献
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引入了广义向量拟平衡问题和广义集值拟平衡问题,得到了W-空间上广义向量拟平衡问题的存在性定理,作为推论,得到了W-空间上四类拟平衡问题的存在性定理,这些结果推广和改进了文献[1-7]的相应结果。 相似文献
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相补理论的研究,首先开始于60年代早期Lemke、Cottle和Dantzig对以及其他作者的一些工作.随后,相补理论大量地应用于数学和工程技术的许多领域,最近,为了研究大量产生于介质渗流、弹性接触、控制与优化、经济与运输平衡以及弹性薄板的临界平衡状态等方面的线性和非线性问题,人们从不同的角度出发把相补理论加以改进和推广(参见[4-11],[13-29]及其参考文献). 相似文献
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本文引进了映射Q相对于另一映射 T 是下半连续的概念。在此条件下,讨论了广义拟变分不等式的选择映射的连续性问题。并得到了一个广义拟变分不等式解的存在性定理。 相似文献
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L-拟序集上的广义Alexandroff拓扑与广义超度量空间上的广义Alexandroff拓扑 总被引:1,自引:1,他引:0
证明[10]中定义的L-拟序集上的广义Alexandroff拓扑是[2]中定义的广义超度量空间上的广义Alexandroff拓扑的推广,并且广义超度量空间中有关广义Alexandroff拓扑的许多性质都可以推广到L-拟序集中。 相似文献
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51.PreliminaryLetXbeaset.Througho11ttl1lspaperweshalldenoteby2xthefaruilyofallsubsetsofX,by(X)thefamilyofallnoneruptyfinitesuhsetsof'X.lfXlsasul,setofavectorspace,co(X)denotestheconvexhu1lofX.IfXisatopologicalspaceandA=X,thenwedenotebyintx(A)theil1teriorofAinXandc.l.(A)theclosureofAinXrespectively.Definitionl.1LetXandYl)etoI3ologicalspacesandT:X-2"isaset-vail1edmapping.(i)Tissaidtobeuppersemicontin\1ous(resp.lowersemicontinuo1Js)atxo6X,ifforeachopensetGinYwithG=T(x,)(resI3.Gn7'(x,… 相似文献
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In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study
generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized
vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized
vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP))
is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone
maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These
existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results
of this paper extend recent results in the literature. They are obtained in a more general setting. 相似文献
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一般多值混合隐拟变分不等式的解的存在性与算法 总被引:3,自引:0,他引:3
引入了实Hilbert空间中一类新的一般多值混合隐拟变分不等式.它概括了丁协平教授引入与研究过的熟知的广义混合隐拟变分不等式类成特例.运用辅助变分原理技巧来解这类一般多值混合隐拟变分不等式.首先,定义了具真凸下半连续的二元泛函的新的辅助变分不等式,并选取了一适当的泛函,使得其唯一的最小值点等价于此辅助变分不等式的解.其次,利用此辅助变分不等式,构造了用于计算一般多值混合隐拟变分不等式逼近解的新的迭代算法.在此,等价性保证了算法能够生成一列逼近解.最后,证明了一般多值混合隐拟变分不等式解的存在性与逼近解的收敛性.而且,给算法提供了新的收敛判据.因此,结果对M.A.Noor提出的公开问题给出了一个肯定答案,并推广和改进了关于各种变分不等式与补问题的早期与最近的结果,包括最近文献中涉及单值与集值映象的有关混合变分不等式、混合拟变不等式与拟补问题的相应结果. 相似文献
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In this paper, we consider the implicit quasi-variational inequality without continuity assumptions of data mappings. Our approach here is completely different from the one based on KKM theorem in the literature. Interesting applications to generalized quasi-variational inequalities for both discontinuous mappings and discontinuous fuzzy mappings are given.This paper was partially supported by the NSC grant no. 86-2115-M-110-004. 相似文献
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《Mathematical and Computer Modelling》1999,29(5):1-11
In this paper, we introduce and study a new class of variational inequalities, which is called the set-valued mixed quasi-variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued mixed quasi-variational inequalities, fixed-point problems and the set-valued implicit resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. 相似文献
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《Optimization》2012,61(4):515-526
In this article, we established some solution existence theorems for implicit quasivariational inequalities. We first established some results in finite-dimensional spaces and then a solution existence result in infinite-dimensional spaces was derived. Our theorems are proved for discontinuous mappings and sets which may be unbounded. The results presented in this article are improvements of results in Cubiotti, and Yao (Cubiotti, P. and Yao, J.C., 1997, Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings. Mathematical Methods of Operations Research, 46, 213–328; Cubiotti, P. and Yao, J.C., 2007, Discontinuous implicit generalized quasi-variational inequalities in Banach spaces. Journal of Global Optimization (To appear)) 相似文献
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考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果. 相似文献
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In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given. 相似文献
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Suhel Ahmad Khan 《Journal of Global Optimization》2011,49(4):695-705
In this paper, we introduce and study a generalized class of vector implicit quasi complementarity problem and the corresponding
vector implicit quasi variational inequality problem. By using Fan-KKM theorem, we derive existence of solutions of generalized
vector implicit quasi variational inequalities without any monotonicity assumption and establish the equivalence between those
problems in Banach spaces. 相似文献
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In this paper, we first generalize a foundational quasi-variational inequality (Theorem 3) which plays a key role throughout this paper by relaxing the compactness condition. Then we set up general forms of (generalized) quasi-variational inequalities and obtain a series of existence theorems without the compactness assumption. Also, since many other quasi-variational inequalities in the literature are special cases of ours, they can be generalized by our results. 相似文献
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L. C. Ceng S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2008,137(1):121-133
In this paper, we consider a generalized vector variational-like inequality problem (for short, GVVLIP), which includes generalized
vector variational inequalities, vector variational inequalities and classical variational inequalities as special cases.
The concepts of generalized C-pseudomonotone-like and generalized H-hemicontinuous-like operators are introduced. Some existence results for GVVLIP are obtained under the assumptions of generalized
C-pseudomonotone-like property and generalized H-hemicontinuous-like property. These results appear to be new and interesting. New existence results of the classical variational
inequality are also obtained.
In this research, the first author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers
in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai. The third author was partially
supported by Grant NSC 94-2213-E-110-035. 相似文献