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1.
In this paper, we introduce and study a hybrid extragradient method for finding solutions of a general variational inequality
problem with inverse-strongly monotone mapping in a real Hilbert space. An iterative algorithm is proposed by virtue of the
hybrid extragradient method. Under two sets of quite mild conditions, we prove the strong convergence of this iterative algorithm
to the unique common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general
variational inequality problem, respectively.
L. C. Zeng’s research was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation
of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality grant (075105118).
J. C. Yao’s research was partially supported by a grant from the National Science Council of Taiwan. 相似文献
2.
Asymmetric variational inequality problems over product sets: Applications and iterative methods 总被引:5,自引:0,他引:5
Jong-Shi Pang 《Mathematical Programming》1985,31(2):206-219
In this paper, we (i) describe how several equilibrium problems can be uniformly modelled by a finite-dimensional asymmetric
variational inequality defined over a Cartesian product of sets, and (ii) investigate the local and global convergence of
various iterative methods for solving such a variational inequality problem. Because of the special Cartesian product structure,
these iterative methods decompose the original variational inequality problem into a sequence of simpler variational inequality
subproblems in lower dimensions. The resulting decomposition schemes often have a natural interpretation as some adjustment
processes.
This research was based on work supported by the National Science Foundation under grant ECS 811–4571. 相似文献
3.
J. S. Pang 《Journal of Optimization Theory and Applications》1990,66(1):121-135
In this paper, we derive some further differentiability properties of solutions to a parametric variational inequality problem defined over a polyhedral set. We discuss how these results can be used to establish the feasibility of continuation of Newton's method for solving the variational problem in question.This work was based on research supported by the National Science Foundation under Grant No. ECS-87-17968. 相似文献
4.
Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems 总被引:1,自引:0,他引:1
We generalize the concept of well-posedness to a mixed variational inequality and give some characterizations of its well-posedness.
Under suitable conditions, we prove that the well-posedness of a mixed variational inequality is equivalent to the well-posedness
of a corresponding inclusion problem. We also discuss the relations between the well- posedness of a mixed variational inequality
and the well-posedness of a fixed point problem. Finally, we derive some conditions under which a mixed variational inequality
is well-posed.
This work was supported by the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the
Doctoral Program of Higher Education (20060610005). The research of the third author was partially support by NSC 95-2221-E-110-078. 相似文献
5.
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
6.
This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued
variational inclusion problems. Characterization of strong convergence of this iterative method is established.
L. C. Ceng’s research 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.
S. Schaible’s research partially supported by the National Science Council of Taiwan.
This research was partially supported by the grant NSC 96-2628-E-110-014-MY3. 相似文献
7.
In this paper, we give a hybrid extragradient iterative method for finding the approximate element of the common set of solutions of a generalized equilibrium problem, a system of variational inequality problems, a variational inequality problem and a fixed point problem for a strictly pseudocontractive mapping in a real Hilbert space. Further we establish a strong convergence theorem based on this method. The results presented in this paper improves and generalizes the results given in Yao et al. [36] and Ceng et al. [7], and some known corresponding results in the literature. 相似文献
8.
In this paper, we study a class of general monotone equilibrium problems in a real Hilbert space which involves a monotone differentiable bifunction. For such a bifunction, a skew-symmetric type property with respect to the partial gradients is established. We suggest to solve this class of equilibrium problems with the modified combined relaxation method involving an auxiliary procedure. We prove the existence and uniqueness of the solution to the auxiliary variational inequality in the auxiliary procedure. Further, we prove also the weak convergence of the modified combined relaxation method by virtue of the monotonicity and the skew-symmetric type property.Communicated by F. GiannessiHis research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and by the Dawn Program Foundation in Shanghai.His research was partially supported by a grant from the National Science Council of Taiwan. 相似文献
9.
In this note, the Auslender gap function, which is used to formulate a variational inequality into an equivalent minimization problem, is shown to be differentiable in the generalized sense and has a lower contingent derivative under suitable conditions. This enables us to establish necessary and sufficient conditions for the existence of a solution to problems of variational inequalities.This research was partially supported by the National Natural Science Foundation of China and the Research Committee of Hong Kong Polytechnic University.
Communicated by F. Giannessi 相似文献
10.
In this paper, we introduce an iterative method to approximate a common solution of a split equilibrium problem, a variational inequality problem and a fixed point problem for a nonexpansive mapping in real Hilbert spaces. We prove that the sequences generated by the iterative scheme converge strongly to a common solution of the split equilibrium problem, the variational inequality problem and the fixed point problem for a nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. 相似文献
11.
Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities 总被引:3,自引:0,他引:3
Lu-Chuan Ceng Chang-yu Wang Jen-Chih Yao 《Mathematical Methods of Operations Research》2008,67(3):375-390
In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational
inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities
is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle
for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient
method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we
provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.
J.-C. Yao’s research was partially supported by a grant from the National Science Council. 相似文献
12.
Iterative methods for variational and complementarity problems 总被引:12,自引:0,他引:12
In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.This research was based on work supported by the National Science Foundation under grant ECS-7926320. 相似文献
13.
In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American
options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem
is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown
that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order.
This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter.
A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the
theoretical findings and to show the effectiveness and usefulness of the method.
This work was partially supported by a research grant from the University of Western Australia and the Research Grant Council
of Hong Kong, Grants PolyU BQ475 and PolyU BQ493. 相似文献
14.
David Kinderlehrer 《Applied Mathematics and Optimization》1982,8(1):159-188
The Signorini problem for an elastic body admits a convenient formulation as a variational inequality. However, it is not coercive. In this note we establish a priori limitations for the solution, estimates of the contact set, and stability for the solution of this problem. The last section is devoted to the example of an infinite circular cylinder, in plane strain.This research was partially supported by the N. S. F. 相似文献
15.
L. C. Zeng S. Schaible J. C. Yao 《Journal of Optimization Theory and Applications》2005,124(3):725-738
The auxiliary principle technique is extended to study the generalized strongly nonlinear mixed variational-like inequality problem for set-valued mappings without compact values. We establish first the existence of a solution of the related auxiliary problem. Then, the iterative algorithm for solving that problem is given by using this existence result. Moreover, the existence of a solution of the original problem and the convergence of iterative sequences generated by the algorithm are both derived.Research 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, China. Research partially supported by a grant from the National Science Council
of Taiwan 相似文献
16.
Narin Petrot 《Journal of Applied Mathematics and Computing》2010,32(2):393-404
The purpose of this paper is to suggest and analyze a number of iterative algorithms for solving the generalized set-valued variational inequalities in the sense of Noor in Hilbert spaces. Moreover, we show some relationships between the generalized set-valued variational inequality problem in the sense of Noor and the generalized set-valued Wiener-Hopf equations involving continuous operator. Consequently, by using the equivalence, we also establish some methods for finding the solutions of generalized set-valued Wiener-Hopf equations involving continuous operator. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory. 相似文献
17.
S. Schaible J. C. Yao L. C. Zeng 《Journal of Optimization Theory and Applications》2006,129(3):425-436
This paper introduces an iterative method for finding approximate solutions of a set-valued mixed quasivariational inequality in the setting of a Banach space. Existence of a solution of this rather general problem and the convergence of the proposed iterative method to a solution are established.The first two authors were partially supported by the National Science Council of the Republic of China. The third author was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and by the Dawn Program Foundation in ShanghaiCommunicated by 相似文献
18.
On vector variational inequalities 总被引:11,自引:0,他引:11
In this paper, we study vector variational inequalities. The concept of weaklyC-pseudomonotone operator is introduced. By employing the Fan lemma, we establish several existence results. The new results extend and unify existence results of vector variational inequalities for monotone operators under a Banach space setting. In particular, existence results for the generalized vector complementarity problem with weaklyC-pseudomonotone operators in Banach space are obtained.This research was partially supported by the National Science Council of the Republic of China under Contract NSC 84-2121-M-110-008. 相似文献
19.
Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games 总被引:1,自引:0,他引:1
The noncooperative multi-leader-follower game can be formulated as a generalized Nash equilibrium problem where each player solves a nonconvex mathematical program with equilibrium constraints. Two major deficiencies exist with such a formulation: One is that the resulting Nash equilibrium may not exist, due to the nonconvexity in each players problem; the other is that such a nonconvex Nash game is computationally intractable. In order to obtain a viable formulation that is amenable to practical solution, we introduce a class of remedial models for the multi-leader-follower game that can be formulated as generalized Nash games with convexified strategy sets. In turn, a game of the latter kind can be formulated as a quasi-variational inequality for whose solution we develop an iterative penalty method. We establish the convergence of the method, which involves solving a sequence of penalized variational inequalities, under a set of modest assumptions. We also discuss some oligopolistic competition models in electric power markets that lead to multi-leader-follower games.Jong-Shi Pang: The work of this authors research was partially supported by the National Science Foundation under grant CCR-0098013 and ECS-0080577 and by the Office of Naval Research under grant N00014-02-1-0286.Masao Fukushima: The work of this authors research was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Culture and Sports of Japan. 相似文献
20.
L. C. Ceng G. Mastroeni J. C. Yao 《Journal of Optimization Theory and Applications》2008,137(3):485-495
By means of generalized KKM theory, we prove a result on the existence of solutions and we establish general variational principles,
that is, vector optimization formulations of set-valued maps for vector generalized systems. A perturbation function is involved
in general variational principles. We extend the theory of gap functions for vector variational inequalities to vector generalized
systems and we prove that the solution sets of the related vector optimization problems of set-valued maps contain the solution
sets of vector generalized systems. A further vector optimization problem is defined in such a way that its solution set coincides
with the solution set of a weak vector generalized system.
Research carried on within the agreement between National Sun Yat-Sen University of Kaohsiung, Taiwan and Pisa University,
Pisa, Italy, 2007.
L.C. Ceng research was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation
of Ministry of Education of China (20070270004), and Science and Technology Commission of Shanghai Municipality grant (075105118).
J.C. Yao research was partially supported by the National Science Center for Theoretical Sciences at Tainan. 相似文献