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《Optimization》2012,61(4):485-499
An existence result for the equilibrium problem is proved in a general topological vector space. As applications, existence results are derived for variational inequality problems, vector equilibrium problems and vector variational inequality problems. Our results extend and unify a number of existence theorems in non-compact cases 相似文献
3.
Lan Zhao 《Annals of Operations Research》1993,44(2):173-193
In this paper we use the theory of variational inequalities to study the general economic equilibrium problem with production. The variational inequality is defined on a bounded set. Existence, uniqueness and sensitivity of the equilibrium point (pair of price vector and activity vector) are discussed through studying this variational inequality. 相似文献
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在FC-空间中引入和研究了一类广义向量变分型不等式(GVVTIP),包含了大多数向量平衡问题,向量变分不等式问题,广义向量平衡问题和广义向量变分不等式问题作为特殊情况.利用F-KKM定理,在非紧FC-空间中,建立了关于GVVTIP解的某些新的存在定理.这些定理统一、改进和推广了文献中的一些重要的已知结果. 相似文献
5.
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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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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引进Stampacchia向量均衡问题与一种新的向量相补问题.用数值方法,得到它们的存在定理,并讨论Stampacchia广义向量变分不等式,向量隐相补问题与极小元问题的关系. 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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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
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Generalized convex functions preserve many valuable properties of mathematical programming problems with convex functions. Generalized monotone maps allow for an extension of existence results for variational inequality problems with monotone maps. Both models are special realizations of an abstract equilibrium problem with numerous applications, especially in equilibrium analysis (e.g., Blum and Oettli, 1994). We survey existence results for equilibrium problems obtained under generalized convexity and generalized monotonicity. We consider both the scalar and the vector case. Finally existence results for a system of vector equilibrium problems under generalized convexity are surveyed which have applications to a system of vector variational inequality problems. Throughout the survey we demonstrate that the results can be obtained without the rigid assumptions of convexity and monotonicity. 相似文献
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Generalized convex functions preserve many valuable properties of mathematical programming problems with convex functions. Generalized monotone maps allow for an extension of existence results for variational inequality problems with monotone maps. Both models are special realizations of an abstract equilibrium problem with numerous applications, especially in equilibrium analysis (e.g., Blum and Oettli, 1994). We survey existence results for equilibrium problems obtained under generalized convexity and generalized monotonicity. We consider both the scalar and the vector case. Finally existence results for a system of vector equilibrium problems under generalized convexity are surveyed which have applications to a system of vector variational inequality problems. Throughout the survey we demonstrate that the results can be obtained without the rigid assumptions of convexity and monotonicity. 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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A method of duality for a mixed vector equilibrium problem 总被引:1,自引:0,他引:1
In this paper, a dual scheme for a mixed vector equilibrium problem is introduced by using the method of Fenchel conjugate
function. Under the stabilization condition, the relationships between the solutions of mixed vector equilibrium problem (MVEP)
and dual mixed vector equilibrium problem (DMVEP) are discussed. Moreover, under the same condition, the solutions of MVEP
and DMVEP are proved relating to the saddle points of an associated Lagrangian mapping. As applications, this dual scheme
is applied to vector convex optimization and vector variational inequality. 相似文献
14.
F. Raciti 《Journal of Global Optimization》2008,40(1-3):353-360
Since a look to the present literature shows that the notion of vector equilibrium is not univocally defined, the relationship
between vector equilibrium problems and vector variational inequalities deserves a specific analysis, deeper than in the scalar
case. We analyse and compare various definitions and clarify how they depend on the modelling of the problem under consideration.
Furthermore, we show that at least one vector variational inequality formulation of the problem is possible, which is equivalent
to a Wardrop-type equilibrium condition. The analysis is illustrated through the concrete example of a multiclass and multiobjective
supply demand network.
相似文献
15.
From Scalar to Vector Equilibrium Problems in the Quasimonotone Case 总被引:15,自引:0,他引:15
In a unified approach, existence results for quasimonotone vector equilibrium problems and quasimonotone (multivalued) vector variational inequality problems are derived from an existence result for a scalar equilibrium problem involving two (rather than one) quasimonotone bifunctions. The results in the vector case are not only obtained in a new way, but they are also stronger versions of earlier existence results. 相似文献
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本文引入一般多值向量变分不等式问题(GMVVI),这推广和统一了现有的向量变分不等式,文内还引入了弱C-伪单调映射和半连续映的概念,在弱C-伪单调性和半连续性的假设下,给出了(GMVVI)的广义线性化引理和解的存在定理,本文的结果即使对一般向量变分不等式问题和广义向量变分不等式问题也是全新的。 相似文献
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Generalized Vector Equilibrium Problems in Generalized Convex Spaces 总被引:14,自引:3,他引:11
In this paper, we introduce and study a class of abstract generalized vector equilibrium problems (AGVEP) in generalized convex spaces which includes most vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems, and generalized vector variational inequality problems as special cases. By using the generalized GKKM and generalized SKKM type theorems due to the first author, some new existence results of equilibrium points for the AGVEP are established in noncompact generalized convex spaces. As consequences, some recent results in the literature are obtained under much weaker assumptions. 相似文献
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The purpose of this paper is to establish optimality conditions for vector equilibrium problems with constraints. By using
the separation of convex sets, we obtain the necessary and sufficient conditions for the Henig efficient solution and the
superefficient solution to the vector equilibrium problem with constraints. As applications of our results, we derive some
optimality conditions to the vector variational inequality problem and the vector optimization problem with constraints. 相似文献
19.
Yunan Wu Yuchen Peng Long Peng Ling Xu 《Journal of Optimization Theory and Applications》2012,153(2):485-496
The super efficiency of a vector variational inequality is considered in this paper. We show that for both the single and
multiple criteria cases, a network equilibrium model can be recast as super efficient solutions to a kind of variational inequality.
For the network equilibrium model with a vector-valued cost function, we derive the necessary and sufficient condition in
terms of the super efficiency of a vector variational inequality by using the Gerstewitz’s function without any convex assumptions. 相似文献
20.
Characterizations of Solutions for Vector Equilibrium Problems 总被引:5,自引:0,他引:5
Ansari Q.H. Konnov I.V. Yao J.C. 《Journal of Optimization Theory and Applications》2002,113(3):435-447
In this paper, we characterize the solutions of vector equilibrium problems as well as dual vector equilibrium problems. We establish also vector optimization problem formulations of set-valued maps for vector equilibrium problems and dual vector equilibrium problems, which include vector variational inequality problems and vector complementarity problems. The set-valued maps involved in our formulations depend on the data of the vector equilibrium problems, but not on their solution sets. We prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of the vector equilibrium problems. 相似文献