论文标题
线性系统和线性可行性问题的惩罚和增强kaczmarz方法
Penalty & Augmented Kaczmarz Methods For Linear Systems & Linear Feasibility Problems
论文作者
论文摘要
在这项工作中，我们从优化的角度阐明了用于求解线性系统（LS）和线性可行性（LF）问题的所谓的Kaczmarz方法。我们介绍了众所周知的优化方法，例如Lagrangian惩罚和随机Kaczmarz（RK）方法的增强Lagrangian。在此过程中，我们提出了RK方法的两个变体，即随机惩罚Kacmarz（RPK）方法和随机增强Kacmarz（RAK）方法。我们对所提出的方法进行收敛分析，并获得线性收敛结果。
In this work, we shed light on the so-called Kaczmarz method for solving Linear System (LS) and Linear Feasibility (LF) problems from a optimization point of view. We introduce well-known optimization approaches such as Lagrangian penalty and Augmented Lagrangian in the Randomized Kaczmarz (RK) method. In doing so, we propose two variants of the RK method namely the Randomized Penalty Kacmarz (RPK) method and Randomized Augmented Kacmarz (RAK) method. We carry out convergence analysis of the proposed methods and obtain linear convergence results.
