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1.
S. Al-Homidan Q. H. Ansari S. Schaible 《Journal of Optimization Theory and Applications》2007,134(3):515-531
We consider five different types of systems of generalized vector variational inequalities and derive relationships among
them. We introduce the concept of pseudomonotonicity for a family of multivalued maps and prove the existence of weak solutions
of these problems under these pseudomonotonicity assumptions in the setting of Hausdorff topological vector spaces as well
as real Banach spaces. We also establish the existence of a strong solution of our problems under lower semicontinuity for
a family of multivalued maps involved in the formulation of the problems. By using a nonlinear scalar function, we introduce
gap functions for our problems by which we can solve systems of generalized vector variational inequalities using optimization
techniques.
The first two authors were supported by SABIC and Fast Track Research Grants SAB-2006-05. They are grateful to the Department
of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research
facilities. 相似文献
2.
The purpose of this paper is to study the solvability for a class of generalized vector variational inequalities in reflexive Banach spaces. Utilizing the KKM-Fan lemma and the Nadler’s result, we prove the solvability results for this class of generalized vector variational inequalities for monotone vector multifuctions. On the other hand, we first introduce the concepts of complete semicontinuity and strong semicontinuity for vector multifunctions. Then we prove the solvability for this class of generalized vector variational inequalities without monotonicity assumption by using these concepts and by applying the Brouwer fixed point theorem. The results in this paper are extension and improvement of the corresponding results in Huang and Fang (2006). 相似文献
3.
On Implicit Vector Variational Inequalities 总被引:5,自引:0,他引:5
In this paper, we study the existence of solutions of implicit vector variational inequalities for multifunctions. Generalized pseudomonotonicity concepts are introduced. Our results extend and unify corresponding earlier existence results of many authors for vector variational inequalities under the Hausdorff topological vector space setting. 相似文献
4.
This paper considers the existence of solutions and the equivalence of four kinds of vector variational inequalities (VVI). More precisely, a sufficient condition is provided under which the solution sets of these VVIs are nonempty and equal. An example is given, showing that such a sufficient condition is essential to ensure the results. Actually, the main theorems in this paper can be regarded as a suitable correction and a refinement of recent results due to Chang et al. (Ref. 1). 相似文献
5.
Gwinner变分不等式和隐变分不等式 总被引:2,自引:0,他引:2
本文在研究Gwinner变分不等式的基础上,利用新的集值映象不动点定理,探讨一类具广泛意义的隐变分不等式问题,改进了迄今相关结果中对紧性条件的要求,在非紧设置下获得了解的存在性定理. 相似文献
6.
Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities 总被引:3,自引:0,他引:3
The variational inequality problem with set-valued mappings is very useful in economics and nonsmooth optimization. In this paper, we study the existence of solutions and the formulation of solution methods for vector variational inequalities (VVI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence of a solution of the VVI. It is shown that the optimization problem formulated by using gap functions can be transformed into a semi-infinite programming problem. We investigate also the existence of a solution for the generalized VVI with a set-valued mapping by virtue of the existence of a solution of the VVI with a single-valued function and a continuous selection theorem. 相似文献
7.
Technical Note Discontinuous Implicit Quasivariational Inequalities in Normed Spaces 总被引:1,自引:0,他引:1
In this paper, we consider an implicit quasivariational inequality without continuity assumptions in normed spaces. The main
result (Theorem 2.1) provides an infinite-dimensional version of Theorem 3.2 in Ref. 1. To achieve such a goal, we employ
Theorem 3.2 in Ref. 1 and the technique of Cubiotti in Ref. 2. In particular, Theorem 3.1 covers a recent result of Cubiotti
(Theorem 3.1 of Ref. 2) as a special case.
Communicated by F. Giannessi
This research was partially supported by the National Science Council of Taiwan, ROC. 相似文献
8.
Generalized Vector Variational Inequalities 总被引:6,自引:0,他引:6
In this paper, we introduce a generalized vector variational inequality problem (GVVIP) which extends and unifies vector variational inequalities as well as classical variational inequalities in the literature. The concepts of generalized C-pseudomonotone and generalized hemicontinuous operators are introduced. Some existence results for GVVIP are obtained with the assumptions of generalized C-pseudomonotonicity and generalized hemicontinuity. These results appear to be new and interesting. New existence results of the classical variational inequality are also obtained. 相似文献
9.
Q. H. Ansari Z. Khan A. H. Siddiqi 《Journal of Optimization Theory and Applications》2005,127(2):263-283
In this paper, we introduce weighted variational inequalities over product of sets and system of weighted variational inequalities.
It is noted that the weighted variational inequality problem over product of sets and the problem of system of weighted variational
inequalities are equivalent. We give a relationship between system of weighted variational inequalities and systems of vector
variational inequalities. We define several kinds of weighted monotonicities and establish several existence results for the
solution of the above-mentioned problems under these weighted monotonicities. We introduce also the weighted generalized variational
inequalities over product of sets, that is, weighted variational inequalities for multivalued maps and systems of weighted
generalized variational inequalities. Extensions of weighted monotonicities for multivalued maps are also considered. The
existence of a solution of weighted generalized variational inequalities over product of sets is also studied. The existence
results for a solution of weighted generalized variational inequality problem give also the existence of solutions of systems
of generalized vector variational inequalities.
The first and third author express their thanks to the Department of Mathematical Sciences, King Fahd University of Petroleum
and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities. The authors are also grateful to the referees
for comments and suggestions improving the final draft of this paper. 相似文献
10.
Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem 总被引:6,自引:0,他引:6
The concepts of monotone pair of mappings and vector implicit complementarity problem (VICP) in ordered Banach spaces are introduced. Existence theorems for simultaneous vector variational inequalities (VVI) and VICP are proved. 相似文献
11.
12.
G. P. Crespi A. Guerraggio M. Rocca 《Journal of Optimization Theory and Applications》2007,132(1):213-226
In this paper, we give notions of well posedness for a vector optimization problem and a vector variational inequality of
the differential type. First, the basic properties of well-posed vector optimization problems are studied and the case of
C-quasiconvex problems is explored. Further, we investigate the links between the well posedness of a vector optimization problem
and of a vector variational inequality. We show that, under the convexity of the objective function f, the two notions coincide. These results extend properties which are well known in scalar optimization.
Communicated by F. Giannessi 相似文献
13.
A systematic study of the upper semicontinuity and the lower semicontinuity of the solution map in parametric affine variational
inequalities is given in this paper. Several examples are constructed to analyze the results.
This work was supported by Korea Research Foundation Grant (KRF 2001-015-DP0049), the APEC Postdoctoral Fellowships Program,
and the KOSEF Brain Pool Program. 相似文献
14.
本文研究一类广义隐式向量拟变分不等式问题,利用Fan-Kakutani不动点定理证明其解存在,推广了相关的文献中的结论. 相似文献
15.
16.
L. C. Ceng S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2008,137(1):121-133
In this paper, we consider a generalized vector variational-like inequality problem (for short, GVVLIP), which includes generalized
vector variational inequalities, vector variational inequalities and classical variational inequalities as special cases.
The concepts of generalized C-pseudomonotone-like and generalized H-hemicontinuous-like operators are introduced. Some existence results for GVVLIP are obtained under the assumptions of generalized
C-pseudomonotone-like property and generalized H-hemicontinuous-like property. These results appear to be new and interesting. New existence results of the classical variational
inequality are also obtained.
In this research, the first author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers
in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai. The third author was partially
supported by Grant NSC 94-2213-E-110-035. 相似文献
17.
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
18.
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
19.
P. Cubiotti 《Journal of Optimization Theory and Applications》1997,92(3):457-475
In this paper, we deal with the following problem: given a real normed space E with topological dual E*, a closed convex set XE, two multifunctions :X2X and
, find
such that
We extend to the above problem a result established by Ricceri for the case (x)X, where in particular the multifunction is required only to satisfy the following very general assumption: each set (x) is nonempty, convex, and weakly-star compact, and for each yX–:X the set
is compactly closed. Our result also gives a partial affirmative answer to a conjecture raised by Ricceri himself. 相似文献
20.
B. T. Kien N. C. Wong J. C. Yao 《Journal of Optimization Theory and Applications》2007,135(3):515-530
We study the following generalized quasivariational inequality problem: given a closed convex set X in a normed space E with the dual E
*, a multifunction
and a multifunction Γ:X→2
X
, find a point
such that
,
. We prove some existence theorems in which Φ may be discontinuous, X may be unbounded, and Γ is not assumed to be Hausdorff lower semicontinuous.
The authors express their sincere gratitude to the referees for helpful suggestions and comments.
This research was partially supported by a grant from the National Science Council of Taiwan, ROC.
B.T. Kien was on leave from National University of Civil Engineering, Hanoi, Vietnam. 相似文献