7 papers
Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems
Zeyu Dong, Aqin Xiao, Guojian Yin +1
Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomize…
A Relaxed Randomized Averaging Block Extended Bregman-Kaczmarz Method for Combined Optimization Problems
Zeyu Dong, Aqin Xiao, Guojian Yin +1
Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability i…
A fast block nonlinear Bregman-Kaczmarz method with averaging for nonlinear sparse signal recovery
Aqin Xiao, Xiangyu Gao, Jun-Feng Yin
Recovery of a sparse signal from a nonlinear system arises in many practical applications including compressive sensing, image reconstruction and machine learning. In this paper, a…
Greedy randomized Bregman-Kaczmarz method for constrained nonlinear systems of equations
Aqin Xiao, Junfeng Yin
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 e…
On multi-step extended maximum residual Kaczmarz method for solving large inconsistent linear systems
Aqin Xiao, Junfeng Yin, Ning Zheng
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations techniq…
On averaging block Kaczmarz methods for solving nonlinear systems of equations
Aqin Xiao, Junfeng Yin
A class of averaging block nonlinear Kaczmarz methods is developed for the solution of the nonlinear system of equations. The convergence theory of the proposed method is establish…
On fast greedy block Kaczmarz methods for solving large consistent linear systems
Aqin Xiao, Junfeng Yin, Ning Zheng
A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical anal…