共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the stability of the set of solutions for symmetric vector quasi-equilibrium problems is discussed. Then, we
prove a generic stability theorem and give an existence theorem for essentially connected components of the set of solutions
for symmetric vector quasi-equilibrium problems. Finally, we apply these results to vector weak saddle point problems with
constraints.
This research was partially supported by the Natural Science Foundation of China (Grant number: 10561007) and Natural Science
Foundation of Jiangxi Province, China. 相似文献
2.
This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the
gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem
for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector
quasi-equilibrium problems are established.
This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the
National Natural Science Foundation of China. 相似文献
3.
Jun-Yi Fu 《Journal of Mathematical Analysis and Applications》2003,285(2):708-713
The symmetric vector quasi-equilibrium problem is introduced. Under suitable assumptions, the symmetric vector quasi-equilibrium problem is solvable. As its applications, a coincidence point theorem and the existence of vector optimization problem for a pair of vector-valued mappings are reduced. 相似文献
4.
Ali P. Farajzadeh 《Journal of Mathematical Analysis and Applications》2006,322(2):1099-1110
In this paper we, using a particular technique, consider the symmetric vector quasi-equilibrium problems in the Hausdorff topological vector space. As applications of our existence theorem, a coincidence point theorem and the existence of vector optimization problem for a pair of vector-valued mappings are obtained. Moreover, we answer an open question raised by Fu in [J.Y. Fu, Symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl. 285 (2003) 708-713]. 相似文献
5.
《Optimization》2012,61(7):1537-1545
In this paper, we introduce generalized Levitin–Polyak well-posedness of symmetric strong vector quasi-equilibrium problem. We give characterizations for generalized Levitin–Polyak well-posedness of the symmetric strong vector quasi-equilibrium problem and the symmetric weak vector quasi-equilibrium problem by closed graph of the approximating solution mapping. Our results improve the main result presented in Zhang. 相似文献
6.
Generalized vector quasi-equilibrium problems 总被引:3,自引:0,他引:3
7.
In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions. 相似文献
8.
In the paper, existence theorems for two classes of generalized vector quasi-equilibrium problems are established by using
a fixed point theorem and some examples are given to illustrate them. An application to vector quasi-optimization problems
is shown.
This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 60574073 and 10471142). 相似文献
9.
In this paper, we first give a vector-valued version of Brézis and Browder’s scalar general principle. We then apply the vector-valued
general principle to study a vector Ekeland’s variational principle in a F-type topological space, which unifies and improves the corresponding vector-valued Ekeland’s variational results in complete
metric space.
This project was partially supported by the Research Grants Council of Hong Kong (BG771) and National Natural Science Foundation
of China (70501015, 70401006). 相似文献
10.
In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibrium problem for vector-valued functions. As an application, we derive some existence results for a solution to the Debreu type equilibrium problem for vector-valued functions. 相似文献
11.
在拓扑向量空间中,利用Ky Fan截口定理得到一个锥凸向量拟均衡问题弱Pareto解的存在性结果.作为该结果的应用,得到了一个对称向量拟均衡问题在支付映射为锥凸条件下弱Pareto解的存在性定理.该定理在较弱的条件下回答了Fu在文献[1]中提出的第二个问题,即在支付映射为锥凸且连续的条件下对称向量拟均衡问题的弱Pareto解是否存在.最后在赋范线性空间中研究了锥凸对称向量拟均衡问题弱Pareto解集的通有稳定性. 相似文献
12.
Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems 总被引:3,自引:0,他引:3
X. H. Gong 《Journal of Optimization Theory and Applications》2007,133(2):151-161
In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium
problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient
solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show
the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector
equilibrium problem.
This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation
of Jinxing Province, China. 相似文献
13.
Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search 总被引:1,自引:0,他引:1
In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for
short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that
the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms
for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally
complementary solution to the monotone SCCP under some assumptions.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010) and Natural Science
Foundation of Tianjin (Grant No. 07JCYBJC05200) 相似文献
14.
Lü Fang 《数学学报(英文版)》1992,8(2):189-203
In this paper it will be shown that the spectrum of every unicellular unilateral weighted shift operator on a symmetric Banach
space is the singleton set {0}. From this, we give an affirmative answer to Rosenthal-Shields' problem.
Project supported by the National Natural Science Foundation of China 相似文献
15.
The paper deals with a generalization of a vector quasivariational inequality. An existence theorem for its solutions is established; it is based on a kind of minimax inequality, which is here established for continuous affine mappings and differs from previous results. Fan's section theorem for set-valued mappings is extended. An application for an equilibrium problem of a network with vector-valued cost functions is given.This research was supported by the National Nature Science Foundation of China. 相似文献
16.
17.
In this paper, three kinds of conjugate dual problems are constructed by virtue of different perturbations to a constrained
vector optimization problem. Weak duality, strong duality, and some inclusion relations for the image sets of the three dual
problems are established.
This research was partially supported by the National Natural Science Foundation of China (Grant Number 60574073) and the
Natural Science Foundation Project of CQ CSTC (Grant Number 2007BB6117). The authors thank two anonymous referees for valuable
comments and suggestions, which helped improving the paper. 相似文献
18.
X. H. Gong 《Journal of Optimization Theory and Applications》2008,139(1):35-46
In this paper, we obtain some stability results for parametric weak vector equilibrium problems in topological vector spaces.
We provide sufficient conditions for the continuity of the solution set mapping in parametric weak monotone vector equilibrium
problems.
This research was partially supported by the National Natural Science Foundation of China (Grant 10561007) and the Natural
Science Foundation of Jiangxi Province, China. 相似文献
19.
J. Y. Fu 《Journal of Optimization Theory and Applications》2006,128(3):605-619
In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi 相似文献
20.
In this paper, two types of Levitin–Polyak well-posedness of vector equilibrium problems with variable domination structures
are investigated. Criteria and characterizations for two types of Levitin–Polyak well-posedness of vector equilibrium problems
are shown. Moreover, by virtue of a gap function for vector equilibrium problems, the equivalent relations between the Levitin–Polyak
well-posedness for an optimization problem and the Levitin–Polyak well-posedness for a vector equilibrium problem are obtained.
This research was partially supported by the National Natural Science Foundation of China (Grant number: 60574073) and Natural
Science Foundation Project of CQ CSTC (Grant number: 2007BB6117). 相似文献