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

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.