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1.
Chih-Sheng Chuang 《Optimization》2016,65(4):859-876
Split variational inclusion problem is an important problem, and it is a generalization of the split feasibility problem. In this paper, we present feasible algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for these algorithms. As application, we study the split feasibility problem in real Hilbert spaces. Final, numerical results are given for our main results. 相似文献
2.
《Optimization》2012,61(12):2339-2367
ABSTRACTIn this paper, we suggest two new iterative methods for finding an element of the solution set of split variational inclusion problem in real Hilbert spaces. Under suitable conditions, we present weak and strong convergence theorems for these methods. We also apply the proposed algorithms to study the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view. 相似文献
3.
《Mathematical Methods in the Applied Sciences》2018,41(2):826-838
The purpose of this paper is the presentation of a new extragradient algorithm in 2‐uniformly convex real Banach spaces. We prove that the sequences generated by this algorithm converge strongly to a point in the solution set of split feasibility problem, which is also a common element of the solution set of a generalized equilibrium problem and fixed points of of two relatively nonexpansive mappings. We give a numerical example to investigate the behavior of the sequences generated by our algorithm. 相似文献
4.
《Optimization》2012,61(6):929-944
The purpose of this article is to investigate the problem of finding a common element of the set of fixed points of a non-expansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a hybrid Mann iterative scheme with perturbed mapping which is based on the well-known Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also construct an iterative process for finding a common fixed point of two mappings, one of which is non-expansive and the other taken from the more general class of Lipschitz pseudocontractive mappings. 相似文献
5.
6.
A new method for a class of linear variational inequalities 总被引:14,自引:0,他引:14
In this paper we introduce a new iterative scheme for the numerical solution of a class of linear variational inequalities. Each iteration of the method consists essentially only of a projection to a closed convex set and two matrix-vector multiplications. Both the method and the convergence proof are very simple.This work is supported by the National Natural Science Foundation of the P.R. China and NSF of Jiangsu. 相似文献
7.
Mohammad Eslamian 《Optimization》2016,65(2):443-465
In the first part of this paper, we present a new general algorithm for solving the split common fixed point problem for an infinite family of demicontractive mappings. We establish strong convergence of the algorithm in an infinite dimensional Hilbert space. As applications, we consider algorithms for split variational inequality problem and split common null point problem. In the second part of this paper, we present a new algorithm and strong convergence theorem for approximation of solutions of split equality fixed point problems for an infinite family of demicontractive mappings. Our results improve and generalize some recent results in the literature. 相似文献
8.
Chung-Chien Hong 《Optimization》2016,65(10):1867-1883
In this article we devise two iteration schemes for approximating common fixed points of a finite family of nonexpansive mappings and establish the corresponding strong convergence theorem for the sequence generated by any one of our algorithms. Then we apply our results to approximate a solution of the so-called constrained multiple-set convex feasibility fixed point problem for firmly nonexpansive mappings which covers the multiple-set convex feasibility problem in the literature. In particular, our algorithms can be used to approximate the zero point problem of maximal monotone operators, and the equilibrium problem. Furthermore, the unique minimum norm solution can be obtained through our algorithms for each mentioned problem. 相似文献
9.
《Optimization》2012,61(5):553-573
Implicit and explicit viscosity methods for finding common solutions of equilibrium and hierarchical fixed points are presented. These methods are used to solve systems of equilibrium problems and variational inequalities where the involving operators are complements of nonexpansive mappings. The results here are situated on the lines of the research of the corresponding results of Moudafi [Krasnoselski-Mann iteration for hierarchical fixed-point problems, Inverse Probl. 23 (2007), pp. 1635–1640; Weak convergence theorems for nonexpansive mappings and equilibrium problems, to appear in JNCA], Moudafi and Maingé [Towards viscosity approximations of hierarchical fixed-points problems, Fixed Point Theory Appl. Art ID 95453 (2006), 10 pp.; Strong convergence of an iterative method for hierarchical fixed point problems, Pac. J. Optim. 3 (2007), pp. 529–538; Coupling viscosity methods with the extragradient algorithm for solving equilibrium problems, to appear in JNCA], Yao and Liou [Weak and strong convergence of Krasnosel'ski?–Mann iteration for hierarchical fixed point problems, Inverse Probl. 24 (2008), 015015 8 pp.], S. Takahashi and W. Takahashi [Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006), pp. 506–515], Xu [Viscosity method for hierarchical fixed point approach to variational inequalities, preprint.], Combettes and Hirstoaga [Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005), pp. 117–136] and Plubtieng and Pumbaeang [A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 336 (2007), pp. 455–469.]. 相似文献
10.
《Optimization》2012,61(6):873-885
Many problems to appear in signal processing have been formulated as the variational inequality problem over the fixed point set of a nonexpansive mapping. In particular, convex optimization problems over the fixed point set are discussed, and operators which are considered to the problems satisfy the monotonicity. Hence, the uniqueness of the solution of the problem is not always guaranteed. In this article, we present the variational inequality problem for a monotone, hemicontinuous operator over the fixed point set of a firmly nonexpansive mapping. The main aim of the article is to solve the proposed problem by using an iterative algorithm. To this goal, we present a new iterative algorithm for the proposed problem and its convergence analysis. Numerical examples for the proposed algorithm for convex optimization problems over the fixed point set are provided in the final section. 相似文献
11.
《Optimization》2012,61(9):1841-1854
We introduce a new iteration method for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of strict pseudocontractions in a real Hilbert space. The weak convergence of the iterative sequences generated by the method is obtained thanks to improve and extend some recent results under the assumptions that the cost mapping associated with the variational inequality problem only is pseudomonotone and not necessarily inverse strongly monotone. Finally, we present some numerical examples to illustrate the behaviour of the proposed algorithm. 相似文献
12.
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
13.
The aim of this paper is to study the penalty method for solving a class of stochastic differential variational inequalities (SDVIs). The penalty problem for solving SDVIs is first constructed and the convergence of the sequences generated by the penalty problem is proved under some mild conditions. As an application, the convergence of the sequences generated by the penalty problem is obtained for solving a stochastic migration equilibrium problem with movement cost. 相似文献
14.
I. V. Konnov 《Computational Mathematics and Mathematical Physics》2006,46(7):1186-1192
A descent method with a gap function is proposed for a finite-dimensional variational inequality with nonintegrable and nonsmooth
mapping. The convergence of the method with line search is established under strong monotonicity conditions on the underlying
mapping.
Published in Russian in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 7, pp. 1251–1257.
This article was translated by the author. 相似文献
15.
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
16.
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
17.
Steepest‐descent proximal point algorithms for a class of variational inequalities in Banach spaces
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《Mathematische Nachrichten》2018,291(8-9):1191-1207
In this paper, we present a new approach to the problem of finding a common zero for a system of m‐accretive mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. We propose an implicit iteration method and two explicit ones, based on compositions of resolvents with the steepest‐descent method. We show that our results contain some iterative methods in literature as special cases. An extension of the Xu's regularization method for the proximal point algorithm from Hilbert spaces onto Banach ones under simple conditions of convergence and a new variant for the method of alternating resolvents are obtained. Numerical experiments are given to affirm efficiency of the methods. 相似文献
18.
In this paper, a class of bi-level variational inequalities for describing some practical equilibrium problems, which especially
arise from engineering, management and economics, is presented, and a neural network approach for solving the bi-level variational
inequalities is proposed. The energy function and neural dynamics of the proposed neural network are defined in this paper,
and then the existence of the solution and the asymptotic stability of the neural network are shown. The simulation algorithm
is presented and the performance of the proposed neural network approach is demonstrated by some numerical examples. 相似文献
19.
20.
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