共查询到20条相似文献,搜索用时 484 毫秒
1.
Min Li 《Numerical Functional Analysis & Optimization》2013,34(3):310-322
An algorithm for solving nonlinear monotone equations is proposed, which combines a modified Liu-Storey conjugate gradient method with hyperplane projection method. Under mild conditions, the global convergence of the proposed method is established with a suitable line search method. The method can be applied to solve large-scale problems for its lower storage requirement. Numerical results indicate that our method is efficient. 相似文献
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Pengjie Liu Xiaoyu Wu Hu Shao Yan Zhang Shuhan Cao 《Numerical Linear Algebra with Applications》2023,30(2):e2471
In this work, by considering the hyperplane projection and hybrid techniques, three scaled three-term conjugate gradient methods are extended to solve the system of constrained monotone nonlinear equations, and the developed methods have the advantages of low storage and only using function values. The new methods satisfy the sufficient descent condition independent of any line search criterion. It has been proved that three new methods converge globally under some mild conditions. The numerical experiments for constrained monotone nonlinear equations and image de-blurring problems illustrate that the proposed methods are numerically effective and efficient. 相似文献
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本文在著名PRP共轭梯度算法的基础上研究了一种无导数谱PRP投影算法,并证明了算法在求解带有凸约束条件的非线性单调方程组问题的全局收敛性.由于无导数和储存量小的特性,它更适应于求解大规模非光滑的非线性单调方程组问题.数值试验表明,新算法对给定的测试问题是有效的和稳定的. 相似文献
4.
借助谱梯度法和HS共轭梯度法的结构, 建立一种求解非线性单调方程组问题的谱HS投影算法. 该算法继承了谱梯度法和共轭梯度法储存量小和计算简单的特征,
且不需要任何导数信息, 因此它适应于求解大规模非光滑的非线性单调方程组问题. 在适当的条件下, 证明了该算法的收敛性, 并通过数值实验表明了该算法的有效性. 相似文献
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陈香萍 《数学的实践与认识》2017,(13):168-175
推广了一种修正的CG_DESCENT共轭梯度方法,并建立了一种有效求解非线性单调方程组问题的无导数投影算法.在适当的线搜索条件下,证明了算法的全局收敛性.由于新算法不需要借助任何导数信息,故它适应于求解大规模非光滑的非线性单调方程组问题.大量的数值试验表明,新算法对给定的测试问题是有效的. 相似文献
7.
Based on a modified line search scheme, this paper presents a new derivative-free projection method for solving nonlinear monotone equations with convex constraints, which can be regarded as an extension of the scaled conjugate gradient method and the projection method. Under appropriate conditions, the global convergence and linear convergence rate of the proposed method is proven. Preliminary numerical results are also reported to show that this method is promising. 相似文献
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Hideaki Iiduka 《Applied mathematics and computation》2011,217(13):6315-6327
Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm. 相似文献
12.
Many problems arising from machine learning, compressive sensing, linear inverse problem, and statistical inference involve finding sparse solutions to under-determined or ill-conditioned equations. In this paper, a gradient projection method is proposed to recover sparse signal in compressive sensing by solving the nonlinear convex constrained equations. The global convergence is established with the backtracking line search. Preliminary numerical experiments coping with the sparse signal reconstruction in compressive sensing are performed, which show that the proposed method is very effective and stable. 相似文献
13.
Since 1965, there has been significant progress in the theoretical study on quasi-Newton methods for solving nonlinear equations, especially in the local convergence analysis. However, the study on global convergence of quasi-Newton methods is relatively fewer, especially for the BFGS method. To ensure global convergence, some merit function such as the squared norm merit function is typically used. In this paper, we propose an algorithm for solving nonlinear monotone equations, which combines the BFGS method and the hyperplane projection method. We also prove that the proposed BFGS method converges globally if the equation is monotone and Lipschitz continuous without differentiability requirement on the equation, which makes it possible to solve some nonsmooth equations. An attractive property of the proposed method is that its global convergence is independent of any merit function.We also report some numerical results to show efficiency of the proposed method.
14.
Jinkui Liu & Shengjie Li 《计算数学(英文版)》2015,33(4):341-355
In this paper, we propose a spectral DY-type projection method for nonlinear monotone systems of equations, which is a reasonable combination of DY conjugate gradient method, the spectral gradient method and the projection technique. Without the differentiability assumption on the system of equations, we establish the global convergence of the proposed method, which does not rely on any merit function. Furthermore, this method is derivative-free and so is very suitable to solve large-scale nonlinear monotone systems. The preliminary numerical results show the feasibility and effectiveness of the proposed method. 相似文献
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本文研究了约束矩阵方程问题中异类约束解的迭代算法.利用修正共轭梯度法,求得了特殊双变量线性矩阵方程组的异类约束解,选取特殊的初始矩阵,得到唯一极小范数异类约束解.理论证明和数值算例验证了该方法的有限步收敛性,推广了修正共轭梯度法在求约束矩阵方程问题中的应用范围. 相似文献
16.
Sindhu Narayanan & P. Kaelo 《高等学校计算数学学报(英文版)》2021,14(2):527-539
Conjugate gradient methods are interesting iterative methods that solve
large scale unconstrained optimization problems. A lot of recent research has thus
focussed on developing a number of conjugate gradient methods that are more effective. In this paper, we propose another hybrid conjugate gradient method as a linear
combination of Dai-Yuan (DY) method and the Hestenes-Stiefel (HS) method. The
sufficient descent condition and the global convergence of this method are established using the generalized Wolfe line search conditions. Compared to the other
conjugate gradient methods, the proposed method gives good numerical results and
is effective. 相似文献
17.
In this paper, we propose a projection method for solving a system of nonlinear monotone equations with convex constraints.
Under standard assumptions, we show the global convergence and the linear convergence rate of the proposed algorithm. Preliminary
numerical experiments show that this method is efficient and promising.
This work was supported by the Postdoctoral Fellowship of The Hong Kong Polytechnic University, the NSF of Shandong China
(Y2003A02). 相似文献
18.
共轭梯度法是一类具有广泛应用的求解大规模无约束优化问题的方法. 提出了一种新的非线性共轭梯度(CG)法,理论分析显示新算法在多种线搜索条件下具有充分下降性. 进一步证明了新CG算法的全局收敛性定理. 最后,进行了大量数值实验,其结果表明与传统的几类CG方法相比,新算法具有更为高效的计算性能. 相似文献
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基于修正拟牛顿方程,利用Goldstein-Levitin-Polyak(GLP)投影技术,建立了求解带凸集约束的优化问题的两阶段步长非单调变尺度梯度投影算法,证明了算法的全局收敛性和一定条件下的Q超线性收敛速率.数值结果表明新算法是有效的,适合求解大规模问题. 相似文献
20.
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