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1.
Some existence results for vector quasivariational inequalities with multifunctions in Banach spaces are derived by employing
the KKM-Fan theorem. In particular, we generalize a result by Lin, Yang and Yao, and avoid monotonicity assumptions. We also
consider a new quasivariational inequality problem and propose notions of weak and strong equilibria while applying the results
to traffic network problems. 相似文献
2.
We consider a weak vector generalized quasivariational inequality. By introducing a method of scalarization which does not require any assumption on the data and by using previous results of the authors concerning scalar generalized quasivariational inequalities, we present Kuhn-Tucker-like conditions for this problem in the case in which the set-valued operator of the constraints is defined by a finite number of inequalities 相似文献
3.
In this paper, we further study a class of generalized constrained multiobjective games where the number of players may be finite or infinite, the strategy sets may be general FC-spaces without local convexity structure, and all payoff functions get their values in infinite-dimensional topological vector spaces. By using an existence theorem of maximal elements for a family of set-valued mappings in FC-spaces due to the author, an existence theorem of solutions for a system of generalized vector quasivariational inclusions is first proved in general FC-spaces. By applying the existence result of solutions of the system of generalized vector quasivariational inclusions, some existence theorems of (weak) Pareto equilibria for the generalized constrained multiobjective games are established in noncompact product FC-spaces. Some special cases of our results are also discussed. Our results are new and different from the corresponding known results in the literature. 相似文献
4.
Phan Quoc Khanh Lai Jiu Lin Vo Si Trong Long 《Mathematical Methods of Operations Research》2014,79(3):253-272
In this paper, we establish a continuous selection theorem and use it to derive five equivalent results on the existence of fixed points, sectional points, maximal elements, intersection points and solutions of variational relations, all in topological settings without linear structures. Then, we study the solution existence of a number of optimization-related problems as examples of applications of these results: quasivariational inclusions, Stampacchia-type vector equilibrium problems, Nash equilibria, traffic networks, saddle points, constrained minimization, and abstract economies. 相似文献
5.
Upper Semicontinuity of the Solution set to Parametric Vector Quasivariational Inequalities 总被引:4,自引:0,他引:4
We prove the upper semicontinuity (in term of the closedness) of the solution set with respect to parameters of vector quasivariational
inequalities involving multifunctions in topological vector spaces under the semicontinuity of the data, avoiding monotonicity
assumptions. In particular, a new quasivariational inequality problem is proposed. Applications to quasi-complementarity problems
are considered
This work was partially supported by the program “Optimisation et Mathématiques Appliquées” of C.I.U.F-C.U.D./C.U.I. of Belgium
and by the National Basic Research Program in Natural Sciences of NCSR of Vietnam 相似文献
6.
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
7.
Nguyen Van Hung Vo Minh Tam Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(7):4614-4626
In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new. 相似文献
8.
I. P. Ryazantseva 《Differential Equations》2008,44(7):1006-1017
For quasivariational inequalities of special form in a Hilbert space, we construct a continuous second-order method and a discrete version of this method, prove the strong convergence of these methods, and indicate the possibility of obtaining estimates for the convergence rate. We separately study the convergence of the continuous method under the assumption that the operators describing the quasivariational inequality to be solved are potential. We establish sufficient conditions for the unique solvability of the nonlinear problems determining these methods. 相似文献
9.
In this paper, we study a class of implicit vector variational inequalities which contain implicit variational inequalities and generalized quasivariational inequalities as special cases. By employing the Fan–Kakutani fixed-point theorem and the Oettli scalarization procedure, respectively, we establish several existence results for implicit vector variational inequalities. 相似文献
10.
Wei-Shih Du 《Journal of Global Optimization》2010,47(1):119-132
In this paper, we first establish the existence theorems of the solution of hybrid inclusion and disclusion systems, from
which we study mixed types of systems of generalized quasivariational inclusion and disclusion problems and systems of generalized
vector quasiequilibrium problems. Some applications of existence theorems to feasible points for various mathematical programs
with variational constraints or equilibrium constraints, system of vector saddle point and system of minimax theorem are also
given. 相似文献
11.
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
12.
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
13.
Hölder continuity and uniqueness of the solutions of general multivalued vector quasiequilibrium problems in metric spaces are established. The results are shown to be extensions of recent ones for equilibrium problems with some improvements. Applications in quasivariational inequalities, vector quasioptimization and traffic network problems are provided as examples for others in various optimization—related problems. 相似文献
14.
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
15.
16.
The problem is to minimize a finite collection of objective functions over admissible sets depending on the so-called price vector. The minima in question and the price vector are linked together by a subdifferential governing law. The problem stated as a system of variational–hemivariational inequalities, defined on a nonconvex feasible set, is reduced to one variational–hemivariational inequality involving nonmonotone multivalued mapping. The existence of solutions is examined under the assumption that the constrained functions are positive homogeneous of degree one. The study has been inspired by economic issues and leads to new results concerning the existence of competitive equilibria. 相似文献
17.
M. B. Lignola 《Journal of Optimization Theory and Applications》2006,128(1):119-138
In this paper, two concepts of well-posedness for quasivariational inequalities having a unique solution are introduced. Some
equivalent characterizations of these concepts and classes of well-posed quasivariational inequalities are presented. The
corresponding concepts of well-posedness in the generalized sense are also investigated for quasivariational inequalities
having more than one solution
The author is grateful to an anonymous referee for valuable comments. 相似文献
18.
We consider the semicontinuity of the solution set and the approximate solution set of parametric multivalued quasivariational
inequalities in topological vector spaces. Three kinds of problems arising from the multivalued situation are investigated.
A rather complete picture, which is symmetric for the two kinds of semicontinuity (lower and upper semicontinuity) and for
the three kinds of multivalued quasivariational inequality problems, is supplied. Moreover, we use a simple technique to prove
the results. The results obtained improve several known ones in the literature.
This research was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. The final part
of this work was completed during a stay of the first author at the Department of Mathematics, University of Pau, Pau, France,
and its hospitality is acknowledged. 相似文献
19.
In this paper, we apply new results on variational relation problems obtained by D. T. Luc (J Optim Theory Appl 138:65–76,
2008) to generalized quasi-equilibrium problems. Some sufficient conditions on the existence of its solutions of generalized quasi-equilibrium
problems are shown. As special cases, we obtain several results on the existence of solutions of generalized Pareto and weak
quasi-equilibrium problems concerning C-pseudomonotone multivalued mappings. We deduce also some results on the existence of solutions to generalized vector Pareto
and weakly quasivariational inequality and vector Pareto quasi-optimization problems with multivalued mappings. 相似文献
20.
《Optimization》2012,61(9):1353-1365
In this article, we study the existence of solutions for a quasivariational relation problem and then give applications to the existence of solutions for set-valued Ekeland's principle, generalized vector Ekeland's variational principle and generalized equilibrium problems. Our results and techniques of proof are different from any existence result in the literature. 相似文献