共查询到20条相似文献,搜索用时 171 毫秒
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在拓扑向量空间中讨论下Dini方向导数形式的广义Minty向量似变分不等式问题. 可微形式的Minty变分不等式、Minty似变分不等式和Minty向量变分不等式是其特殊形式. 该文分别讨论了Minty向量似变分不等式的解与径向递减函数, 与向量优化问题的最优解或有效解之间的关系问题, 以及Minty向量似变分不等式的解集的仿射性质. 这些定理推广了文献中Minty变分不等式的一些重要的已知结果. 相似文献
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通过推广α-不变凸函数和G-预不变凸函数,提出了一类非光滑G-α-预不变凸函数,在非光滑G-α-预不变凸条件下讨论非光滑向量优化问题的解与向量似变分不等式问题的解之间的关系,并证明了向量临界点,弱有效点与非光滑向量似变分不等式问题的解是等价的. 相似文献
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一种新的向量互补问题 总被引:1,自引:1,他引:0
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。 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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基于各种Ekeland变分原理的等价形式, 主要研究局部凸空间中给定有界凸子集乘以距离函数为扰动的单调半连续映射的向量Ekeand变分原理的等价性问题. 首先利用局部凸空间中的向量Ekeland变分原理证明了向量Caristi-Kirk不动点定理,向量 Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理. 进一步研究了向量Ekeland变分原理与向量Caristi-Kirk不动点定理,向量Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理的等价性. 相似文献
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向量似变分不等式解的存在性及解集的稳定性 总被引:3,自引:0,他引:3
本文首先得到一类广义向量似变分不等式问题的解的存在性定理,然后利用usco映射的性质,讨论广义向量似变分不等式的解集的通有稳定性,得到大多数(在Baire分类意义下)广义向量似变分不等式问题的解集是稳定的;另外还引入广义向量似变分不等式解集的本质连通区的概念,并证明了满足一定连续性、凸性条件的广义向量似变分不等式的解集至少存在一个本质连通区. 相似文献
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广义向量似变分不等式解集的通有稳定性及本质连通区的存在性 总被引:10,自引:0,他引:10
本文研究广义向量似变分不等式解集的稳定性.证明了在满足一定的连续性和凸 性条件的广义向量似变分不等式问题构成的空间M中,大多数(在Baire分类意下)广 义向量似变分不等式问题的解集是稳定的,并证明了M中的每个广义向量似变分不等式 的解集至少存在一个本质连通区。 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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《Optimization》2012,61(3):355-367
In this article, we consider equivalence properties between various kinds of lexicographic variational inequalities. By employing various concepts of monotonicity, we show that the usual sequential variational inequality is equivalent to the direct lexicographic variational inequality or to the dual lexicographic variational inequality. We establish several existence results for lexicographic variational inequalities. Also, we introduce the lexicographic complementarity problem and establish its equivalence with the lexicographic variational inequality. We illustrate our approach by several examples of applications to vector transportation and vector spatial equilibrium problems. 相似文献
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Efficiency and Henig Efficiency for Vector Equilibrium Problems 总被引:6,自引:0,他引:6
We introduce the concept of Henig efficiency for vector equilibrium problems, and extend scalarization results from vector optimization problems to vector equilibrium problems. Using these scalarization results, we discuss the existence of the efficient solutions and the connectedness of the set of Henig efficient solutions to the vector-valued Hartman–Stampacchia variational inequality. 相似文献
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X. Q. Yang 《Journal of Optimization Theory and Applications》1997,95(3):729-734
The study of a vector variational inequality has been advanced because it has many applications in vector optimization problems and vector equilibrium flows. In this paper, we discuss relations between a solution of a vector variational inequality and a Pareto solution or a properly efficient solution of a vector optimization problem. We show that a vector variational inequality is a necessary and sufficient optimality condition for an efficient solution of the vector pseudolinear optimization problem. 相似文献
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A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems 总被引:1,自引:0,他引:1
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization
problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function
for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear
scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions
for generalized quasi-vector equilibrium problems.
This paper is dedicated to Professor Franco Giannessi for his 68th birthday 相似文献
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利用标量化方法建立对称向量拟均衡问题有效解的存在性定理.作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理. 相似文献
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Ekeland变分原理在最优化理论及应用研究中具有十分重要的作用.利用非线性标量化函数及相应的非凸分离定理建立了基于改进集的集值Ekeland变分原理.新的Ekeland变分原理包含了一些经典的Ekeland变分原理作为其特例. 相似文献
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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
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Preparation of Papers 总被引:8,自引:0,他引:8
We motivate the study of a vector variational inequality by a practical flow equilibrium problem on a network, namely a generalization of the well-known Wardrop equilibrium principle. Both weak and strong forms of the vector variational inequality are discussed and their relationships to a vector optimization problem are established under various convexity assumptions. 相似文献
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Jinlu Li 《Numerical Functional Analysis & Optimization》2019,40(2):178-193
The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach spaces. In this article, we prove the solvability of some nonlinear split vector variational inequality problems by using fixed-point theorems on partially ordered Banach spaces. It is important to notice that in the results obtained in this article, the considered mappings are not required to have any type of continuity and they just satisfy some order-monotonic conditions. Consequently, both the solvability of linear split vector variational inequality problems and vector variational inequality problems will be immediately obtained from the solvability of nonlinear split vector variational inequality problems. We will apply these results to solving nonlinear split vector optimization problems. The underlying spaces of the considered variational inequality problems may just be vector spaces which do not have topological structures, the considered mappings are not required to satisfy any continuity conditions, which just satisfy some order-increasing conditions. 相似文献