共查询到19条相似文献,搜索用时 109 毫秒
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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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在实Hausdorff拓扑向量空间中,引进含参集值向量均衡问题,给出各种有效解的概念.在锥-次类凸的条件下,得到各种有效解的标量化结果.结合集值映射的弱f-性,在适当假设条件下,得到含参集值向量均衡问题各种有效解映射的下半连续性. 相似文献
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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
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研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
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介绍了广义集值隐向量变分不等式问题系统,并且通过Kakutani-Fan-Glicksberg不动点定理,建立了其解的存在性结果;在此基础上,研究了广义集值隐向量变分不等式问题系统的稳定性,建立了其解集本质连通区的存在性结果. 相似文献
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在Banach空间中研究了一类新的变分包含——隐式集值变分包含问题,得到了隐式变分包含解的等价性与存在性命题及其解的扰动算法,推广、改进了国内外近期获得的一些结果. 相似文献
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在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果. 相似文献
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《数学的实践与认识》2016,(23)
利用集值映射的自然拟C-凸性和集值映射的下(-C)-连续性的定义以及Kakutani-Fan-Glicksberg不动点定理,在不要求锥C的对偶锥C~*具有弱*紧基的情况下,建立了集值广义强向量拟均衡问题解的存在性定理.把相关文献中所得的关于单值映射解的存在性结果推广到了集值映射的情形. 相似文献
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In this paper, we study a class of implicit vector variational inequalities which contain implicit variational inequalities and generalized quasivariational inequalities as special cases. By employing the Fan–Kakutani fixed-point theorem and the Oettli scalarization procedure, respectively, we establish several existence results for implicit vector variational inequalities. 相似文献
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We consider an approach to convert vector variational inequalities into an equivalent scalar variational inequality problem
with a set-valued cost mapping. Being based on this property, we give an equivalence result between weak and strong solutions
of set-valued vector variational inequalities and suggest a new gap function for vector variational inequalities. Additional
examples of applications in vector optimization, vector network equilibrium and vector migration equilibrium problems are
also given
Mathematics Subject Classification(2000). 49J40, 65K10, 90C29 相似文献
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《Numerical Functional Analysis & Optimization》2013,34(7-8):815-829
In this paper, we consider implicit vector variational problems which contain vector equilibrium problems and vector variational inequalities as special cases. The existence of solutions of implicit vector variational problems and vector equilibrium problems have been established. As a special case, we derive some existence results for a solution of vector variational inequalities. We also study the duality of implicit vector variational problems and discuss the relationship between solutions of dual and primal problems. Our results on duality contains known results in the literature as special cases. 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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In this paper, we introduce a new class of generalized implicit vector variational-like inequalities in Hausdorff topological vector spaces and Banach spaces which contain implicit vector equilibrium problems, implicit vector variational inequalities and implicit vector complementarity problems as special cases. We derive some new results by using the KKM–Fan theorem, under compact and noncompact assumptions on underlying convex sets. 相似文献
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In this paper, we introduce and study a class of implicit vector equilibrium problems, which includes a number of (scalar) implicit equilibrium problems, implicit variational inequalities, and implicit complementarity problems as special cases. By using KKM-Fan theorem, we prove some new existence theorems of solutions for this kind of implicit vector equilibrium problems in Hausdorff topological vector spaces. Our results extend and unify some corresponding results of several authors. 相似文献
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S. Khoshkhabar-amiranloo 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1429-1440
This paper deals with set-valued vector optimization problems and set-valued vector variational inequalities in topological vector spaces, and provides some scalarization approaches for these problems by means of the polar cone and Gerstewitz’s scalarization functions. 相似文献
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Weak minimizers,minimizers and variational inequalities for set-valued functions. A blooming wreath?
Giovanni P. Crespi 《Optimization》2017,66(12):1973-1989
Recently, necessary and sufficient conditions in terms of variational inequalities have been introduced to characterize minimizers of convex set-valued functions. Similar results have been proved for a weaker concept of minimizers and weaker variational inequalities. The implications are proved using scalarization techniques that eventually provide original problems, not fully equivalent to the set-valued counterparts. Therefore, we try, in the course of this note, to close the network among the various notions proposed. More specifically, we prove that a minimizer is always a weak minimizer, and a solution to the stronger variational inequality always also a solution to the weak variational inequality of the same type. As a special case, we obtain a complete characterization of efficiency and weak efficiency in vector optimization by set-valued variational inequalities and their scalarizations. Indeed, this might eventually prove the usefulness of the set optimization approach to renew the study of vector optimization. 相似文献