论文标题
关于用于求解大规模非线性系统的Kaczmarz-Motzkin方法
On sampling Kaczmarz-Motzkin methods for solving large-scale nonlinear systems
论文作者
论文摘要
在本文中，为了求解大规模的非线性方程，我们提出了一种非线性采样Kaczmarz-Motzkin（NSKM）方法。基于局部切向锥条件和詹森的不平等，我们证明了我们的方法具有两个不同的假设。然后，对于使用凸约束求解非线性方程，我们提出了NSKM方法的两个变体：投影采样Kaczmarz-Motzkin（PSKM）方法和加速的预测采样Kaczmarz-Motzmotzkmkmkin（APSKM）方法。通过使用投影的非专业特性和NSKM方法的收敛性，获得了收敛分析。数值结果表明，与合适尺寸样本的NSKM方法在计算时间方面优于非线性随机Kaczmarz（NRK）方法。 APSKM和PSKM方法对于受约束的非线性问题是实用的，并且有希望。
In this paper, for solving large-scale nonlinear equations we propose a nonlinear sampling Kaczmarz-Motzkin (NSKM) method. Based on the local tangential cone condition and the Jensen's inequality, we prove convergence of our method with two different assumptions. Then, for solving nonlinear equations with the convex constraints we present two variants of the NSKM method: the projected sampling Kaczmarz-Motzkin (PSKM) method and the accelerated projected sampling Kaczmarz-Motzkin (APSKM) method. With the use of the nonexpansive property of the projection and the convergence of the NSKM method, the convergence analysis is obtained. Numerical results show that the NSKM method with the sample of the suitable size outperforms the nonlinear randomized Kaczmarz (NRK) method in terms of calculation times. The APSKM and PSKM methods are practical and promising for the constrained nonlinear problem.
