共查询到20条相似文献,搜索用时 125 毫秒
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投影法是解决多集分裂可行域问题的广泛且有效的研究方法.本文从分裂迭代视角出发,研究了求解张量可行域问题的高效投影分裂迭代方法.首先,利用投影算子将张量分裂可行域问题转化为多线性方程组.然后,借助加速超松弛法和对称(交替)加速超松弛法的高维化处理方式,推广到适合多线性方程组的求解框架.最后,通过对新的张量分裂迭代格式的谱半径的理论分析,证明了算法的收敛性.充分的数值测试验证了算法的有效性. 相似文献
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在本文中,我们引入了非精确均值投影算法来求解多重集非凸分裂可行问题,其中这些非凸集合为半代数邻近正则集合.通过借助著名的Kurdyka-Lojasiewicz不等式理论,我们建立了算法的收敛性. 相似文献
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简金宝 《数学物理学报(A辑)》2001,21(2):268-277
利用SQP方法、广义投影技术和强次可行方(向)法思想,建立不等式约束优化一个新的初始点任意的快速收敛算法. 算法每次迭代仅需解一个总存在可行解的二次子规划,或用广义投影计算“一阶”强次可行下降辅助搜索方向;采用曲线搜索与直线搜索相结合的方法产生步长. 在较温和的条件下,算法具有全局收敛性、强收敛性、超线性与二次收敛性. 给出了算法有效的数值试验. 相似文献
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广义投影型的超线性收敛算法 总被引:1,自引:0,他引:1
该文利用矩阵分解与广义投影等技巧,给出了求解线性约束的非线性规划的一个广义投影型的超线性收敛算法,不需要δ-主动约束与每一步反复计算投影矩阵,避免了计算的数值不稳定性,利用矩阵求逆的递推公式,计算简便,由于采用了非精确搜索,算法实用可行,文中证明了算法具有收敛性及超线性的收敛速度. 相似文献
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梯度投影法是一类有效的约束最优化算法,在最优化领域中占有重要的地位.但是,梯度投影法所采用的投影是正交投影,不包含目标函数和约束函数的二阶导数信息·因而;收敛速度不太令人满意.本文介绍一种共轭投影概念,利用共轭投影构造了一般线性或非线性约束下的共轭投影变尺度算法,并证明了算法在一定条件下具有全局收敛性.由于算法中的共轭投影恰当地包含了目标函数和约束函数的二阶导数信息,因而收敛速度有希望加快.数值试验的结果表明算法是有效的. 相似文献
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§1 引言对于约束条件为非线性的算法而言,具有收敛性的算法是不多的(参见[9])。1971年在[3]中,E.Polak提出了一个关于非线性约束的梯度投影-可行方向法,并证明了收敛性。1981年,章祥荪在[6]中又对E.Polak方法进行了改进。1985年堵丁柱在[7]工中对特定的非精确线搜索给出了一种具有收敛性的关于非线性约束的梯度投影-可行方向法。这些方法较以前那种先对切面做梯度投影,然后再拉回到可行域的传统梯度投影法(参见[2])具有了 相似文献
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本文讨论了多重分裂算法在求解一类非线性方程组的全局收敛性和单侧收敛性.当用研步Newton法来代替求得每个非线性多重分裂子问题的近似解时,同样给出相应收敛性结论.数值算例证实了算法的有效性. 相似文献
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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
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In this paper, we propose a new simultaneous iterative algorithm for solving the split common fixed point problem of directed operators. Inspired by the idea of cyclic iterative algorithm, we also introduce two iterative algorithms which combine the process of cyclic and simultaneous together. Under mild assumptions, we prove convergence of the proposed iterative sequences. As applications, we obtain several iteration schemes to solve the inverse problem of multiple-sets split feasibility problem. Numerical experiments are presented to confirm the efficiency of the proposed iterative algorithms. 相似文献
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The multiple-sets split feasibility problem (MSFP) arises in many areas and it can be unified as a model for many inverse problems where the constraints are required on the solutions in the domain of a linear operator as well as in the operator's range. Some existing algorithms, in order to get the suitable step size, need to compute the largest eigenvalue of the related matrix, estimate the Lipschitz constant, or use some step-size search scheme, which usually requires many inner iterations. In this article, we introduce a successive projection algorithm for solving the multiple-sets split feasibility problem. In each iteration of this algorithm, the step size is directly computed, which is not needed to compute the largest eigenvalue of the matrix or estimate the Lipschitz constant. It also does not need any step-size search scheme. Its theoretical convergence results are also given. 相似文献
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Hideaki Iiduka 《Numerical Functional Analysis & Optimization》2016,37(2):186-205
The split feasibility problem deals with finding a point in a closed convex subset of the domain space of a linear operator such that the image of the point under the linear operator is in a prescribed closed convex subset of the image space. The split feasibility problem and its variants and generalizations have been widely investigated as a means for resolving practical inverse problems in various disciplines. Many iterative algorithms have been proposed for solving the problem. This article discusses a split feasibility problem which does not have a solution, referred to as an inconsistent split feasibility problem. When the closed convex set of the domain space is the absolute set and the closed convex set of the image space is the subsidiary set, it would be reasonable to formulate a compromise solution of the inconsistent split feasibility problem by using a point in the absolute set such that its image of the linear operator is closest to the subsidiary set in terms of the norm. We show that the problem of finding the compromise solution can be expressed as a convex minimization problem over the fixed point set of a nonexpansive mapping and propose an iterative algorithm, with three-term conjugate gradient directions, for solving the minimization problem. 相似文献
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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
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In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc. 相似文献
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Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP’s with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space. 相似文献
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《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