An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications
An Adaptive Prediction-Correction Method for Solving Large-Scale Nonlinear Systems of Monotone Equations with Applications
复制标题
求解大规模非线性单调方程组的自适应预测校正方法及其应用
DOI：
10.1155/2013/619123
复制
发表时间：
2013-01-01
影响因子：
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通讯作者：
Song, Yisheng
中科院分区：
文献类型：
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作者：
Yu, Gaohang;Niu, Shanzhou;Song, Yisheng
本文将多元谱梯度法与投影方法相结合，提出了一种求解大型非线性单调方程组的自适应预测校正方法。该方法具有如下优点：（1）迭代点与解集之间的距离单调递减，是逐步渐进的;（2）全局收敛性与价值函数及其Lipschitz连续性无关;（3）无需导数，存储量小，可用于求解大规模非光滑方程.初步的数值结果表明，该方法是非常有效的。所提出的方法的一些实际应用证明和测试稀疏信号重建，压缩传感，图像反卷积问题。
Combining multivariate spectral gradient method with projection scheme, this paper presents an adaptive prediction-correction method for solving large-scale nonlinear systems of monotone equations. The proposed method possesses some favorable properties: (1) it is progressive step by step, that is, the distance between iterates and the solution set is decreasing monotonically; (2) global convergence result is independent of the merit function and its Lipschitz continuity; (3) it is a derivative-free method and could be applied for solving large-scale nonsmooth equations due to its lower storage requirement. Preliminary numerical results show that the proposed method is very effective. Some practical applications of the proposed method are demonstrated and tested on sparse signal reconstruction, compressed sensing, and image deconvolution problems.