共查询到20条相似文献,搜索用时 328 毫秒
1.
荣祯 《应用泛函分析学报》2012,14(1):109-112
给出了求解单调变分不等式的两类迭代算法.通过解强单调变分不等式子问题,产生两个迭代点列,都弱收敛到变分不等式的解.最后,给出了这两类新算法的收敛性分析. 相似文献
2.
Gibali[J.Nonlinear Anal.Optim.,2015,6(1):41-51]提出了一种解伪单调非Lipschitz连续变分不等式的自适应次梯度外梯度投影算法.其下一迭代点是通过向一个特定的半空间投影来实施.本文通过构造新的下降方向得到了一类新的自适应次梯度外梯度投影算法,并借助于何炳生和廖立志[J.Optim.Theory Appl.,2002,112(1):111-128]中的技巧优化了这些算法的步长.证明了这些算法所生成序列的全局收敛性.数值实验结果表明这类次梯度外梯度投影算法比已有算法受初始点的选取、变分不等式的维数及停止标准的精度的影响更小.而且,从迭代次数及运算所花的时间来看,新的算法均优于Gibali提出的算法. 相似文献
3.
当可行集为一光滑凸函数的下水平集时,文献[Optimization,2020,69(6):1237-1253]提出了一种惯性双次梯度外梯度算法来求解Hilbert空间中的单调且Lipschitz连续的变分不等式问题.该算法在每次迭代中仅需向一个半空间计算两次投影,并得到了算法的弱收敛结果.本文通过使用黏性方法以及在惯性步采用新的步长来修正该算法.在适当的假设条件下证明了新算法所生成的序列能强收敛到变分不等式的一个解.此外,新算法在每次迭代中也仅需向半空间计算两次投影. 相似文献
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求解单调变分不等式问题的一个连续型迭代方法 总被引:1,自引:1,他引:0
本文给出一个求解单调变分不等式问题的连续型迭代方法,对任意单调趋于零的正数序列和任意初始点,方法产生的迭代点列均收敛到所求变分不等式问题的一个解,且在适当条件下方法具有Q-超线性收敛率.数值试验结果进一步表明了所给方法的稳定性和有效性. 相似文献
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近似邻近点算法是求解单调变分不等式的一个有效方法,该算法通过解决一系列强单调子问题,产生近似邻近点序列来逼近变分不等式的解,而外梯度算法则通过每次迭代中增加一个投影来克服一般投影算法限制太强的缺点,但它们均未能改变迭代步骤中不规则闭凸区域上投影难计算的问题.于是,本文结合外梯度算法的迭代格式,构造包含原投影区域的半空间,将投影建立在半空间上,简化了投影的求解过程,并对新的邻近点序列作相应限制,使得改进的算法具有较好的收敛性. 相似文献
8.
本文讨论Banach空间中子集非紧的情况下的变分不等式数值解.提出了求解相应问题的Ishikawa类迭代算法,证明了算法的子列收敛性和全局收敛性.同时也证明了变分不等式解的存在性. 相似文献
9.
本文在实Hilbert空间上引入了一类求解集值混合变分不等式新的自适应惯性投影次梯度算法.在集值映射T为f-强伪单调或单调的条件下,我们证明了由该自适应惯性投影次梯度算法所产生的序列强收敛于集值混合变分不等式问题的的唯一解. 相似文献
10.
考虑在扰动泛函F是光滑的情况下,利用Bregman距离建立了F-互补问题和广义的变分不等式的等价性,接着假设f是单调映射,给出了这个单调变分不等式的临近点算法,然后给出了算法的收敛性,最后在局部误差界成立的假设下,证明该算法是R-线性收敛的. 相似文献
11.
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
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.
Boris S. Mordukhovich Barbara Panicucci Massimo Pappalardo Mauro Passacantando 《Optimization Letters》2012,6(7):1535-1550
This paper concerns developing two hybrid proximal point methods (PPMs) for finding a common solution of some optimization-related problems. First we construct an algorithm to solve simultaneously an equilibrium problem and a variational inequality problem, combing the extragradient method for variational inequalities with an approximate PPM for equilibrium problems. Next we develop another algorithm based on an alternate approximate PPM for finding a common solution of two different equilibrium problems. We prove the global convergence of both algorithms under pseudomonotonicity assumptions. 相似文献
14.
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
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.
In this paper, we introduce an algorithm as combination between the subgradient extragradient method and inertial method for solving variational inequality problems in Hilbert spaces. The weak convergence of the algorithm is established under standard assumptions imposed on cost operators. The proposed algorithm can be considered as an improvement of the previously known inertial extragradient method over each computational step. The performance of the proposed algorithm is also illustrated by several preliminary numerical experiments. 相似文献
17.
《Optimization》2012,61(2):429-451
Abstract In this paper, new numerical algorithms are introduced for finding the solution of a variational inequality problem whose constraint set is the common elements of the set of fixed points of a demicontractive mapping and the set of solutions of an equilibrium problem for a monotone mapping in a real Hilbert space. The strong convergence of the iterates generated by these algorithms is obtained by combining a viscosity approximation method with an extragradient method. First, this is done when the basic iteration comes directly from the extragradient method, under a Lipschitz-type condition on the equilibrium function. Then, it is shown that this rather strong condition can be omitted when an Armijo-backtracking linesearch is incorporated into the extragradient iteration. The particular case of variational inequality problems is also examined. 相似文献
18.
本文在Hilbert空间上引入了一个新的粘性迭代算法,找到了关于两个逆强单调算子的变分不等式问题的解集与非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了强收敛定理,也给出了一个数值例子.所得结果改进了许多最新结果. 相似文献
19.
《Optimization》2012,61(9):1119-1132
We present two extensions of Korpelevich's extragradient method for solving the variational inequality problem (VIP) in Euclidean space. In the first extension, we replace the second orthogonal projection onto the feasible set of the VIP in Korpelevich's extragradient method with a specific subgradient projection. The second extension allows projections onto the members of an infinite sequence of subsets which epi-converges to the feasible set of the VIP. We show that in both extensions the convergence of the method is preserved and present directions for further research. 相似文献
20.
L. C. Ceng B. S. Mordukhovich J. C. Yao 《Journal of Optimization Theory and Applications》2010,146(2):267-303
This paper studies a general vector optimization problem of finding weakly efficient points for mappings from Hilbert spaces
to arbitrary Banach spaces, where the latter are partially ordered by some closed, convex, and pointed cones with nonempty
interiors. To find solutions of this vector optimization problem, we introduce an auxiliary variational inequality problem
for a monotone and Lipschitz continuous mapping. The approximate proximal method in vector optimization is extended to develop
a hybrid approximate proximal method for the general vector optimization problem under consideration by combining an extragradient
method to find a solution of the variational inequality problem and an approximate proximal point method for finding a root
of a maximal monotone operator. In this hybrid approximate proximal method, the subproblems consist of finding approximate
solutions to the variational inequality problem for monotone and Lipschitz continuous mapping, and then finding weakly efficient
points for a suitable regularization of the original mapping. We present both absolute and relative versions of our hybrid
algorithm in which the subproblems are solved only approximately. The weak convergence of the generated sequence to a weak
efficient point is established under quite mild assumptions. In addition, we develop some extensions of our hybrid algorithms
for vector optimization by using Bregman-type functions. 相似文献