Penalty & Augmented Kaczmarz Methods For Linear Systems & Linear Feasibility Problems
Optimization and Control
2022-08-15 v3 Numerical Analysis
Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2205.08085,
title = {Penalty & Augmented Kaczmarz Methods For Linear Systems & Linear Feasibility Problems},
author = {Md Sarowar Morshed},
journal= {arXiv preprint arXiv:2205.08085},
year = {2022}
}