共查询到20条相似文献,搜索用时 31 毫秒
1.
《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
2.
在Hilbert空间中提出一种新的迭代算法,用于寻求带扰动映像的广义平衡问题与k-严格伪压缩映像的不动点问题的公共解.此外,证明了由此迭代算法生成的序列的强收敛性.所得到的结果,推广并改进了最近一些人所发布的新结果. 相似文献
3.
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
4.
In this paper, we propose a double projection algorithm for a generalized variational inequality with a multi-valued mapping. Under standard conditions, our method is proved to be globally convergent to a solution of the variational inequality problem. Moreover, we present a unified framework of projection-type methods for multi-valued variational inequalities. Preliminary computational experience is also reported. 相似文献
5.
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
6.
In this paper, we introduce a new projection-based algorithm for solving variational inequality problems with a Lipschitz continuous pseudo-monotone mapping in Hilbert spaces. We prove a strong convergence of the generated sequences. The numerical behaviors of the proposed algorithm on test problems are illustrated and compared with previously known algorithms. 相似文献
7.
In this paper, we consider power control for the uplink of a direct-sequence code-division multiple-access data network. In
the uplink, the purpose of power control is for each user to transmit enough power so that it can achieve the required quality
of service without causing unnecessary interference to other users in the system. One method that has been very successful
in solving this purpose for power control is the game-theoretic approach. The problem for power control is modified as a Nash
equilibrium problem in which each user can choose its transmit power in order to maximize its own utility, and a Nash equilibrium
is an ideal solution of the power-control game. We present a noncooperative power-control game in which each user can choose
the transmit power in a way that it gets the sufficient signal-to-interference-plus-noise ratio and maximizes its own utility.
To ensure the existence of a solution, we also propose the variational inequality problem which is connected with the proposed
game. On a linear receiver, we deal with the matched filter receiver. Next we present a new ergodic algorithm for the proposed
power control because the existing iterative algorithms can not be applied effectively to the proposed power control. We also
present convergence analysis for the proposed algorithm. In addition, applying the proposed algorithm to the proposed power
control, we provide numerical examples for the transmit power, the signal-to-interference-plus-noise ratio and so on. Numerical
results for the proposed algorithm shall show that as compared with the existing power-control game and its method, all users
in the network can enjoy the sufficient signal-to-interference-plus-noise ratio and achieve the required quality of service.
相似文献
8.
在Hilbert空间中引进并研究一种新的复合粘性迭代算法,借以寻求有限个平衡问题的公共解集与非扩张映象不动点集的一个公共元素.所得结果改进并推广了最近一些人的最新结果. 相似文献
9.
Chih-Sheng Chuang 《Optimization》2017,66(5):777-792
In this paper, we present hybrid inertial proximal algorithms for the split variational inclusion problems in Hilbert spaces, and provide convergence theorems for the proposed algorithms. In fact, an inertial type algorithm was proposed as an acceleration process. As application, we study split minimization problem, split feasibility problem, relaxed split feasibility problem and linear inverse problem in real Hilbert spaces. Finally, numerical results are given for our main results. 相似文献
10.
In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a monotone mapping. 相似文献
11.
在[1]中,Solodov将非线性互补问题等价地转化成一个带非负约束的优化问题.基于这种转化形式,我们给出了一种求解非线性互补问题的下降算法.在映射为强单调时,证明了算法的全局收敛性. 相似文献
12.
We know that variational inequality problem is very important in the nonlinear analysis. For a variational inequality problem defined over a nonempty fixed point set of a nonexpansive mapping in Hilbert space, the strong convergence theorem has been proposed by I. Yamada. The algorithm in this theorem is named the hybrid steepest descent method. Based on this method, we propose a new weak convergence theorem for zero points of inverse strongly monotone mapping and fixed points of nonexpansive mapping in Hilbert space. Using this result, we obtain some new weak convergence theorems which are useful in nonlinear analysis and optimization problem. 相似文献
13.
Mohammad Eslamian Peyman Eslamian 《Numerical Functional Analysis & Optimization》2016,37(10):1248-1266
In this article, we present a new general algorithm for solving the split common fixed point problem in an infinite dimensional Hilbert space, which is to find a point which belongs to the common fixed point of a family of quasi-nonexpansive mappings such that its image under a linear transformation belongs to the common fixed point of another family of quasi-nonexpansive mappings in the image space. We establish the strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. The algorithm and its convergence results improve and develop previous results in this field. 相似文献
14.
In this paper, we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces. We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions. As an application, the results are applied to solving the zero problem and the equilibrium problem. 相似文献
15.
In this paper, we present an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of an infinite family of nonexpansive mappings and the set of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. 相似文献
16.
本文的目的是在Hilbert空间中引入和研究了一种新的迭代序列,用以寻求具逆一强单调映象的广义平衡问题的解集与无限簇非扩张映象的不动点集的公共元.在适当的条件下,用黏性逼近法证明了逼近于这一公共元的强收敛定理.应用该结论,我们证明了逼近于平衡问题和变分不等式问题的强收敛定理.所得结果改进和推广了文献的相应结果. 相似文献
17.
In this paper, we discuss the visualization of multidimensional data. A well-known procedure for mapping data from a high-dimensional
space onto a lower-dimensional one is Sammon’s mapping. This algorithm preserves as well as possible all interpattern distances.
We investigate an unsupervised backpropagation algorithm to train a multilayer feed-forward neural network (SAMANN) to perform
the Sammon’s nonlinear projection. Sammon mapping has a disadvantage. It lacks generalization, which means that new points
cannot be added to the obtained map without recalculating it. The SAMANN network offers the generalization ability of projecting
new data, which is not present in the original Sammon’s projection algorithm. To save computation time without losing the
mapping quality, we need to select optimal values of control parameters. In our research the emphasis is put on the optimization
of the learning rate. The experiments are carried out both on artificial and real data. Two cases have been analyzed: (1)
training of the SAMANN network with full data set, (2) retraining of the network when the new data points appear. 相似文献
18.
19.
Chih-Sheng Chuang 《Numerical Functional Analysis & Optimization》2017,38(3):306-326
In this article, we study the generalized split variational inclusion problem. For this purpose, motivated by the projected Landweber algorithm for the split equality problem, we first present a simultaneous subgradient extragradient algorithm and give related convergence theorems for the proposed algorithm. Next, motivated by the alternating CQ-algorithm for the split equality problem, we propose another simultaneous subgradient extragradient algorithm to study the general split variational inclusion problem. As applications, we consider the split equality problem, split feasibility problem, split variational inclusion problem, and variational inclusion problem in Hilbert spaces. 相似文献
20.
George C. Hsiao 《Journal of Computational and Applied Mathematics》2011,235(17):4949-4965
In this paper, we are concerned with the error analysis for the finite element solution of the two-dimensional exterior Neumann boundary value problem in acoustics. In particular, we establish explicit priori error estimates in H1 and L2- norms including both the effect of the truncation of the DtN mapping and that of the numerical discretization. To apply the finite element method (FEM) to the exterior problem, the original boundary value problem is reduced to an equivalent nonlocal boundary value problem via a Dirichlet-to-Neumann (DtN) mapping represented in terms of the Fourier expansion series. We discuss essential features of the corresponding variational equation and its modification due to the truncation of the DtN mapping in appropriate function spaces. Numerical tests are presented to validate our theoretical results. 相似文献