Greedy randomized Bregman-Kaczmarz method for constrained nonlinear systems of equations

TL;DR

This paper introduces a greedy randomized Bregman-Kaczmarz method for solving constrained nonlinear systems, demonstrating faster convergence than existing methods through theoretical analysis and numerical experiments.

Contribution

It develops a novel greedy randomized approach with residual-based sampling for nonlinear systems, with proven convergence and improved efficiency.

Findings

Faster convergence compared to existing methods

Theoretical proof of convergence for the proposed algorithms

Numerical experiments confirm effectiveness and efficiency

Abstract

A greedy randomized nonlinear Bregman-Kaczmarz method by sampling the working index with residual information is developed for the solution of the constrained nonlinear system of equations. Theoretical analyses prove the convergence of the greedy randomized nonlinear Bregman-Kaczmarz method and its relaxed version. Numerical experiments verify the effectiveness of the proposed method,which converges faster than the existing nonlinear Bregman-Kaczmarz methods.