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.

翻译：本文针对约束非线性方程组的求解问题，提出了一种通过残差信息采样工作索引的贪婪随机非线性Bregman-Kaczmarz方法。理论分析证明了贪婪随机非线性Bregman-Kaczmarz方法及其松弛版本的收敛性。数值实验验证了所提方法的有效性，其收敛速度优于现有非线性Bregman-Kaczmarz方法。