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1.
《Optimization》2012,61(8):1447-1470
ABSTRACTIn this paper, we introduce a new iterative scheme by combining the hyperplane projection method and the inertial technique for constrained equilibrium problems in real Hilbert spaces. The convergence of the proposed algorithm is established without requiring strict paramonotonicity property. The results presented in the paper extend and improve some recent results in the literature. In addition, a numerical example is given to illustrate the efficiency and performance of the proposed method. 相似文献
2.
《Optimization》2012,61(5):981-998
ABSTRACTIn this paper, we introduce several new extragradient-like approximation methods for solving variational inequalities in Hilbert spaces. Our algorithms are based on Tseng's extragradient method, subgradient extragradient method, inertial method, hybrid projection method and shrinking projection method. Strong convergence theorems are established under appropriate conditions. Our results extend and improve some related results in the literature. In addition, the efficiency of our algorithms is shown through numerical examples which are defined by the hybrid projection methods. 相似文献
3.
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of
a countable family of nonexpansivemappings, the set of an equilibrium problem and the set of solutions of the variational
inequality problem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence
converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected
with Yao, Liou, Yao, Takahashi and many others. 相似文献
4.
Dang Van Hieu 《Applicable analysis》2018,97(5):811-824
The paper proposes a new extragradient algorithm for solving strongly pseudomonotone equilibrium problems which satisfy a Lipschitz-type condition recently introduced by Mastroeni in auxiliary problem principle. The main novelty of the paper is that the algorithm generates the strongly convergent sequences in Hilbert spaces without the prior knowledge of Lipschitz-type constants and any hybrid method. Several numerical experiments on a test problem are also presented to illustrate the convergence of the algorithm. 相似文献
5.
The subgradient extragradient method can be considered as an improvement of the extragradient method for variational inequality problems for the class of monotone and Lipschitz continuous mappings. In this paper, we propose two new algorithms as combination between the subgradient extragradient method and Mann-like method for finding a common element of the solution set of a variational inequality and the fixed point set of a demicontractive mapping. 相似文献
6.
Pham Gia Hung 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6121-6129
We extend the Tikhonov regularization method widely used in optimization and monotone variational inequality studies to equilibrium problems. It is shown that the convergence results obtained from the monotone variational inequality remain valid for the monotone equilibrium problem. For pseudomonotone equilibrium problems, the Tikhonov regularized subproblems have a unique solution only in the limit, but any Tikhonov trajectory tends to the solution of the original problem, which is the unique solution of the strongly monotone equilibrium problem defined on the basis of the regularization bifunction. 相似文献
7.
Dang Van Hieu 《Mathematical Methods in the Applied Sciences》2017,40(11):4065-4079
Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz‐type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
8.
A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping 总被引:5,自引:5,他引:0
The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. 相似文献
9.
10.
Extragradient methods for differential variational inequality problems and linear complementarity systems 下载免费PDF全文
S. Z. Fatemi M. Shamsi Farid Bozorgnia 《Mathematical Methods in the Applied Sciences》2017,40(18):7201-7217
In this paper, 2 extragradient methods for solving differential variational inequality (DVI) problems are presented, and the convergence conditions are derived. It is shown that the presented extragradient methods have weaker convergence conditions in comparison with the basic fixed‐point algorithm for solving DVIs. Then the linear complementarity systems, as an important and practical special case of DVIs, are considered, and the convergence conditions of the presented extragradient methods are adapted for them. In addition, an upper bound for the Lipschitz constant of linear complementarity systems is introduced. This upper bound can be used for adjusting the parameters of the extragradient methods, to accelerate the convergence speed. Finally, 4 illustrative examples are considered to support the theoretical results. 相似文献
11.
Somyot Plubtieng Rattanaporn Punpaeng 《Journal of Mathematical Analysis and Applications》2007,336(1):455-469
In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others. 相似文献
12.
In this paper, we investigate the problem for finding the set of solutions for equilibrium problems, the set of solutions of the variational inequalities for k-Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in a Hilbert space. We introduce a new viscosity extragradient approximation method which is based on the so-called viscosity approximation method and extragradient method. We show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. Finally, we utilize our results to study some convergence problems for finding the zeros of maximal monotone operators. Our results are generalization and extension of the results of Kumam [P. Kumam, Strong convergence theorems by an extragradient method for solving variational inequalities and equilibrium problems in a Hilbert space, Turk. J. Math. 33 (2009) 85–98], Wangkeeree [R. Wangkeeree, An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings, Fixed Point Theory and Applications, 2008, Article ID 134148, 17 pages, doi:10.1155/2008/134148], Yao et al. [Y. Yao, Y.C. Liou, R. Chen, A general iterative method for an finite family of nonexpansive mappings, Nonlinear Analysis 69 (5–6) (2008) 1644–1654], Qin et al. [X. Qin, M. Shang, Y. Su, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, Nonlinear Analysis (69) (2008) 3897–3909], and many others. 相似文献
13.
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
14.
In this paper, we propose a new composite iterative method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of nonexpansive mappings. Our results improve and extend the corresponding ones announced by many others. 相似文献
15.
In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of common fixed points of two hemi-relatively non-expansive mappings and the set of solutions of an equilibrium problem by the CQ hybrid method in Banach spaces. Our results improve and extend the corresponding results announced by Cheng and Tian [Y. Cheng, M. Tian, Strong convergence theorem by monotone hybrid algorithm for equilibrium problems, hemi-relatively nonexpansive mappings and maximal monotone operators, Fixed Point Theory Appl. 2008 (2008) 12 pages, doi:10.1155/2008/617248], Takahashi and Zembayashi [W. Takahashi, K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively non-expansive mappings, Fixed Point Theory Appl. (2008) doi:10.1155/2008/528476] and some others. 相似文献
16.
ZENGQINGGUANG 《高校应用数学学报(英文版)》1997,12(1):117-125
In this paper, we provide a new generalized gradient projection algorithm for nonlinear programming problems with linear constraints. This algorithm has simple structure and is very practical and stable. Under the weaker assumptions, we have proved the global convergence of our algorithm. 相似文献
17.
《Optimization》2012,61(5):1081-1096
In this paper, we extend a projection-type method for variational inequalities from Euclidean spaces to Hadamard manifolds. The proposed method has the following nice features: (i) the algorithm is well defined whether the solution set of the problem is non-empty or not, under weak assumptions; (ii) if the solution set is non-empty, then the sequence generated by the method is convergent to the solution, which is closest to the initial point; and (iii) the existence of the solutions to variational inequalities can be verified through the behaviour of the generated sequence. The results presented in this paper generalize and improve some known results given in literatures. 相似文献
18.
Minglu Ye 《Optimization》2017,66(7):1119-1134
The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method. 相似文献
19.
20.
An iterative method for finding common solutions of equilibrium and fixed point problems 总被引:1,自引:0,他引:1
Vittorio Colao 《Journal of Mathematical Analysis and Applications》2008,344(1):340-352
We introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem and of the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. 相似文献