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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
2.
The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints. 相似文献
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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
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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
8.
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
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.
In this paper, we establish the existence theorems of simultaneous equilibrium problems. As consequences of our results, we
establish the existence theorem of simultaneous mathematical programs and equilibrium problems and the existence theorems
of generalized vector quasi-saddle point problems. 相似文献
11.
In this paper, we obtain some stability results for generalized vector quasivariational inequality problems. We prove that the solution set is a closed set and establish the upper semicontinuity property of the solution set for perturbed generalized vector quasivariational inequality problems. These results extend those obtained in Ref. 1. We obtain also the lower semicontinuity property of the solution set for perturbed classical variational inequalities. Several examples are given for the illustration of our results. 相似文献
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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
14.
For vector quasivariational inequalities involving multifunctions in topological vector spaces, an existence result is obtained without a monotonicity assumption and with a convergence assumption weaker than semicontinuity. A new type of quasivariational inequality is proposed. Applications to quasicomplementarity problems and traffic network equilibria are considered. In particular, definitions of weak and strong Wardrop equilibria are introduced for the case of multivalued cost functions. 相似文献
15.
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
16.
New Type of Generalized Vector Quasiequilibrium Problem 总被引:1,自引:0,他引:1
J. Y. Fu S. H. Wang Z. D. Huang 《Journal of Optimization Theory and Applications》2007,135(3):643-652
In this paper, we introduce a new type of vector quasiequilibrium problem with set-valued mappings and moving cones. By using
the scalarization method and fixed-point theorem, we obtain its existence theorem. As applications, we derive some existence
theorems for vector variational inequalities and vector complementarity problems.
This work was supported by the National Natural Science Foundation of China. The authors are grateful to Professor X.Q. Yang
and the referees for valuable comments and suggestions improving the original draft. 相似文献
17.
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
18.
In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general setting. We also establish several existence results for generalized variation inequalities and generalized quasi-variational inequalities. 相似文献
19.
In this paper, we consider variational inequalities with pseudomonotone maps which depend on a parameter and study the behavior of their solutions. The main result gives sufficient conditions for the stability of the initial variational inequality problem under small perturbations of the parameter. As an application, we obtain a stability result for a class of parametric optimization problems. 相似文献
20.
Tiziana Cardinali Raffaella Servadei 《Proceedings of the American Mathematical Society》2004,132(8):2339-2349
In this paper we obtain the existence of periodic solutions for nonlinear ``invariance' problems monitored by impulsive differential inclusions subject to impulse effects.