共查询到20条相似文献,搜索用时 844 毫秒
1.
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
2.
《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
3.
Vector complementarity and minimal element problems 总被引:13,自引:0,他引:13
X. Q. Yang 《Journal of Optimization Theory and Applications》1993,77(3):483-495
In this paper, vector complementarity problems are introduced as weak versions of vector variational inequalities in ordered Banach spaces. New dual cones are introduced and proved to be closed. In the sense of efficient point, we prove that the minimal element problem is solvable if a vector variational inequality is solvable; we also prove that any solution of a strong vector variational inequality or positive vector complementarity problem is a solution of the minimal element problem.This work was done while the author was with the Chongqing Institute of Architecture and Engineering, Chongqing, P. R. China. 相似文献
4.
The concept of efficiency is used to formulate duality for nondifferentiable multiobjective variational problems. Wolfe and Mond-Weir type vector dual problems are formulated. By using the generalized Schwarz inequality and a characterization of efficient solution, we established the weak, strong, and converse duality theorems under generalized (F,ρ)-convexity assumptions. 相似文献
5.
6.
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
7.
In this paper, we introduce and study a class of generalized nonlinear vector variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems and so on. Applying maximal element theorem, we prove the existence of its solutions in the setting of locally convex topological vector space. 相似文献
8.
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
9.
This paper deals with the relations between vector variational inequality problems and nonsmooth vector optimization problems using the concept of quasi efficiency. We identify the vector critical points, the weak quasi efficient points and the solutions of the weak vector variational inequality problems under generalized approximate convexity assumptions. To the best of our knowledge such results have not been established till now. 相似文献
10.
In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space. 相似文献
11.
Existence of Solutions to Generalized Vector Quasi-Variational-Like Inequalities with Set-Valued Mappings
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Dapeng Gao & Shiqiang Feng 《数学研究通讯:英文版》2014,30(1):90-96
In this paper, we introduce and study a class of generalized vector quasi-variational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and
generalized vector variational-like inequality problems as special cases. We use the
maximal element theorem with an escaping sequence to prove the existence results of
a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space. 相似文献
12.
We establish two global bounds measuring the distance from any vector to the solution set of the co-coercive variational inequality. To prove our results, we use the fact that the co-coercivity condition is sufficient for the (strong) monotonicity of (perturbed) fixed point and normal maps associated with variational inequalities. 相似文献
13.
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
14.
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
15.
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
16.
In this paper, we introduce a Minty type vector variational inequality, a Stampacchia type vector variational inequality, and the weak forms of them, which are all defined by means of subdifferentials on Hadamard manifolds. We also study the equivalent relations between the vector variational inequalities and nonsmooth convex vector optimization problems. By using the equivalent relations and an analogous to KKM lemma, we give some existence theorems for weakly efficient solutions of convex vector optimization problems under relaxed compact assumptions. 相似文献
17.
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
18.
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
19.
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