共查询到19条相似文献,搜索用时 62 毫秒
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推广LCG共轭梯度方法并建立一种求解凸约束非线性单调方程组问题的无导数投影方法.在适当的条件下,证明了方法的全局收敛性.方法不需要任何导数信息,而且继承了共轭梯度方法储存量小的特征,因此它特别适合求解大规模非光滑的非线性单调方程组问题.大量数值结果和比较表明方法是有效的和稳定的. 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
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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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基于谱梯度法和著名LS共轭梯度法的结构,该文建立了求解凸约束非线性伪单调方程组问题的谱LS型无导数投影算法.通过构建适当的谱参数,该算法在每一次迭代中都能保证搜索方向的充分下降性,并且独立于线搜索条件.在适当的假设条件和经典无导数线搜索条件下,算法具有全局收敛性.通过数值实验发现,该算法继承了LS共轭梯度法优秀的计算性能,并提高了稳定性. 相似文献
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拟牛顿法是求解非线性方程组的一类有效方法.相较于经典的牛顿法,拟牛顿法不需要计算Jacobian矩阵且仍具有超线性收敛性.本文基于BFGS和DFP的迭代公式,构造了新的充分下降方向.将该搜索方向和投影技术相结合,本文提出了无导数低存储的投影算法求解带凸约束的非线性单调方程组并证明了该算法是全局且R-线性收敛的.最后,将该算法用于求解压缩感知问题.实验结果表明,本文所提出的算法具有良好的计算效率和稳定性. 相似文献
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基于非单调自适应信赖域法求解非线性方程组 总被引:1,自引:0,他引:1
本文提出了求解非线性方程组的非单调自适应信赖域法.在适当的条件下证明了非单调自适应信赖域法的局部及全局收敛性质.基本的数值实验表明该方法在处理某些非线性方程组是非常有效的. 相似文献
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提出一种求解强单调非线性方程组的BFGS算法,该算法的一个明显优点是Bκ的条件数比Li-Fukushima^[3]提出的GNBFGS中Bκ的条件数小得多。且该算法是一种无需计算导数的下降算法。在一定的条件下,证明了算法的全局收敛性和超线性收敛性。最后进行数值试验,结果表明,本文算法具有较好的数值结果。而且验证了本文所提出的算法中Bκ的条件数要比GNBFGS算法的条件数小得多。 相似文献
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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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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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一类新的共轭投影梯度算法 总被引:2,自引:0,他引:2
本文利用[5]引进的共轭投影的概念,结合堵丁柱[3]中的思想,提出一类新的共轭梯度投影算法.在一定的条件下,证明了该算法具有全局收敛性和超线性收敛速度. 相似文献
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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
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We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs.This research was supported by the Singapore-MIT Alliance and the Australian Research Council. 相似文献
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Newton迭代是非线性方程求根的一个非常有效的方法,它只需计算一阶导数值,不必计算高阶导数值,且具有二阶的收敛速度.本文给出一个新的迭代公式,只需计算函数值,同样也具有二阶的收敛速度,它具有形式简单,计算量小的特点,数值试验表明该迭代公式是非常有效的. 相似文献