2022/05/17 by Md Sarowar Morshed, Morshed, Md Sarowar
Computer Science · Engineering · Mathematics · #34A25 #65B05 #65K05 #90C05 #90C51 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2205.08085
openalex publication_date 2022/05/17 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28
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.