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1.
The quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown.
As special cases, we obtain several results on the existence of solutions of a general vector ideal (proper, Pareto, weak)
quasi-optimization problems, of quasivariational inequalities, and of vector quasi-equilibrium problems. Further, we prove
theorems on the existence for solutions of the sum of these inclusions. As corollaries, we shall show several results on the
existence of solutions to another problems in the vector optimization problems concerning multivalued mappings.
This work was supported by the National Science Council of the Republic of China and the Academy of Sciences and Technologies
of Vietnam.
The authors wish to express their gratitude to the referees for their valuable suggestions. 相似文献
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N. X. Tan 《Journal of Optimization Theory and Applications》2004,123(3):619-638
Quasivariational inclusion problems are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal, proper, Pareto, weak quasioptimization problems, quasivariational inequalities, and vector quasiequilibrium problems. Further, we prove theorems on the existence for solutions of systems of these inclusions. As a corollary, we obtain an ideal minimax theorem concerning vector functions. 相似文献
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Nguyen Xuan Tan 《Numerical Functional Analysis & Optimization》2018,39(2):233-255
In this paper, we apply our new results on quasi-variational inequality problems to generalized quasi-equilibrium problems. Some su?cient conditions on the existence of solutions are shown. In particular, we establish several results on the existence of solutions to fixed points of separately lower and upper semicontinuous (lower and lower, upper and upper) mappings.These generalize some well-known fixed point theorems obtained by previous authors as Browder and Ky Fan, Wu, et al., etc. 相似文献
7.
Lai-Jiu Lin Qamrul Hasan Ansari Yu-Jen Huang 《Mathematical Methods of Operations Research》2007,65(1):85-98
In this paper, we consider more general forms of generalized vector quasi-equilibrium problems for multivalued maps which
include many known vector quasi-equilibrium problems and generalized vector quasi-variational inequality problems as special
cases. We establish some existence results for solutions of these problems under pseudomonotonicity and u-hemicontinuity/ℓ-hemicontinuity assumptions.
相似文献
8.
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
9.
Lai-jiu Lin 《Journal of Global Optimization》2006,34(1):15-32
In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence
theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also
obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of
the Debreu vector equilibrium problems and the Nash vector equilibrium problems. 相似文献
10.
丁协平 《应用泛函分析学报》2010,12(4):289-304
在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理. 相似文献
11.
Zhi Lin 《Journal of Global Optimization》2006,36(4):627-635
In this paper, we study the system of generalized vector quasi-equilibrium problems, which includes as special cases the system of vector quasi-equilibrium problems and the system of generalized vector equilibrium problems, and establish the existence and essential components of the solution set under perturbations of its best-reply map. Moreover, we also derive a new existence theorem of Ky Fan’s points for a set-valued map. 相似文献
12.
In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results,
we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems
of variational inclusion constraints, bilevel problem with systems of constraints. 相似文献
13.
In this paper, we establish some equivalence relations between coincidence theorems and KKM-type theorems. We also obtain some new coincidence theorems and fixed point theorems. Applying the KKM-type theorems we obtain the existence theorems of generalized vector equilibrium problems. From these results, some existence theorems of generalized vector implicit variational inequality problems are established in this paper. 相似文献
14.
The studies of systems of variational inclusions problems and variational disclusions problems with applications 总被引:1,自引:0,他引:1
In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems. 相似文献
15.
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
16.
Bui Trong Kien Ngai Ching Wong Jen-Chih Yao 《Nonlinear Analysis: Theory, Methods & Applications》2008
It is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems. By using the Ky Fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star-pseudomonotone operators are involved. Our results can be applied to the study of the existence of solutions of vector optimal problems. Some examples are given and analyzed. 相似文献
17.
A.P. Farajzadeh A. Amini-Harandi 《Journal of Mathematical Analysis and Applications》2008,344(2):999-1004
In this paper, generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field. 相似文献
18.
Lai-Jiu Lin 《Journal of Global Optimization》2007,39(4):509-527
In this paper, we prove the existence theorems of two types of systems of variational inclusions problem. From these existence
results, we establish Ekeland’s variational principle on topological vector space, existence theorems of common fixed point,
existence theorems for the semi-infinite problems, mathematical programs with fixed points and equilibrium constraints, and
vector mathematical programs with variational inclusions constraints. 相似文献
19.
抽象经济均衡问题解的存在性及其算法 总被引:3,自引:0,他引:3
本文首先研究一类新的向量均衡问题,利用截口定理与KKM定理两种不同的工具证明此类均衡问题解的存在性,接着,把这类向量均衡问题推广到更为一般的情形,随后讨论了具有上下界的均衡问题,它是由Isac,Sehgal和Singh于1999年提出的一个公开问题,本文在一定条件下获得了一个新的解的存在性定理,并构造了一个迭代算法,讨论了算法的收敛性。 相似文献
20.
In this paper, the solvability of Stampacchia generalized vector quasi-equilibrium problem (in short, GVQEP) with set-valued
mapping is studied. By using continuous selection theorem and fixed point theorems, some existence theorems for (GVQEP) are
obtained without any monotonicity assumption. These theorems unify and improve some results in the recent references. 相似文献