A note on the spectral gradient projection method for nonlinear monotone equations with applications
A note on the spectral gradient projection method for nonlinear monotone equations with applications
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DOI：
10.1007/s40314-020-01151-5
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发表时间：
2020-04
影响因子：
2.6
通讯作者：
A. Abubakar;Poom Kumam;Hassan Mohammad
中科院分区：
文献类型：
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作者：
A. Abubakar;Poom Kumam;Hassan Mohammad
在这项工作中，我们提供了关于求解非线性方程的谱梯度投影方法的注释。受最近用于求解具有凸约束的非线性单调方程的谱梯度法的扩展的启发，在本文中，我们注意到，与谱梯度系数的标准选择结合 Solodov 和 Svaiter 的投影策略（用于单调方程组的全局收敛不精确牛顿法。In：Reformulation：Nonsmooth. Piecewise Smooth）相比，选择搜索方向作为两个不同正谱系数乘以残差向量的凸组合更加有效和鲁棒，半平滑和平滑方法，第 355-369 页 Springer，1998）。在适当的假设下，建立了所提出方法的收敛性。初步数值实验表明该方法是有前景的。在本文中，所提出的方法用于恢复稀疏信号并恢复压缩感知产生的模糊图像。
In this work, we provide a note on the spectral gradient projection method for solving nonlinear equations. Motivated by recent extensions of the spectral gradient method for solving nonlinear monotone equations with convex constraints, in this paper, we note that choosing the search direction as a convex combination of two different positive spectral coefficients multiplied with the residual vector is more efficient and robust compared with the standard choice of spectral gradient coefficients combined with the projection strategy of Solodov and Svaiter (A globally convergent inexact newton method for systems of monotone equations. In: Reformulation: Nonsmooth. Piecewise Smooth, Semismooth and Smoothing Methods, pp 355–369. Springer, 1998). Under suitable assumptions, the convergence of the proposed method is established. Preliminary numerical experiments show that the method is promising. In this paper, the proposed method was used to recover sparse signal and restore blurred image arising from compressive sensing.