arXiv subjects

Junfeng Yin

Publications and source records attributed to Junfeng Yin.

7 recordsLinked to original sources

arXiv2026

Adaptive Randomized Extended Bregman-Kaczmarz Method for Combined Optimization Problems

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 randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method for solving such problems. The proposed method incorporates iteration-wise relaxation parameters that are automatically adjusted using residual information, allowing for more aggressive step sizes without additional manual tuning. We establish a convergence theory for the proposed framework and derive expected linear convergence rate guarantees. Numerical experiments on both synthetic and real data sets for sparse and minimum-norm least-squares problems demonstrate that our aRABEBK method achieves faster convergence and improved robustness compared with state-of-the-art extended Kaczmarz and Bregman-Kaczmarz-type algorithms, including its nonadaptive counterpart.

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arXiv2025

A Relaxed Randomized Averaging Block Extended Bregman-Kaczmarz Method for Combined Optimization Problems

Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or incorporating structural information such as sparsity. In this work, we propose a \emph{relaxed randomized averaging block extended Bregman-Kaczmarz} (rRABEBK) method for solving a broad class of combined optimization problems. The proposed method integrates an averaging block strategy with two relaxation parameters to accelerate convergence and enhance numerical stability. We establish a rigorous convergence theory showing that rRABEBK achieves linear convergence in expectation, with explicit constants that quantify the effect of the relaxation mechanism, and a provably faster rate than the classical randomized extended Bregman-Kaczmarz method. Our method can be readily adapted to sparse least-squares problems and extended to both consistent and inconsistent systems without modification. Complementary numerical experiments corroborate the theoretical findings and demonstrate that rRABEBK significantly outperforms the existing Kaczmarz-type algorithms in terms of both iteration complexity and computational efficiency, highlighting both its practical and theoretical advantages.

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arXiv2024

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

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.

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arXiv2023

On multi-step extended maximum residual Kaczmarz method for solving large inconsistent linear systems

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 technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.

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arXiv2023

On averaging block Kaczmarz methods for solving nonlinear systems of equations

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 established under suitable assumptions and the upper bounds of the convergence rate for the proposed method with both constant stepsize and adaptive stepsize are derived. Numerical experiments are presented to verify the efficiency of the proposed method, which outperforms the existing nonlinear Kaczmarz methods in terms of the number of iteration steps and computational costs.

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arXiv2022

On fast greedy block Kaczmarz methods for solving large consistent linear systems

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 analysis of the convergence of the proposed method is given in detail. Numerical experiments show that the proposed methods are efficient and faster than the existing methods.

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arXiv2022

Restarted randomized surrounding methods for solving large linear equations

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the randomized row selection rule and the expectation convergence rate is also addressed. Numerical experiments further demonstrate that the proposed algorithms are efficient and outperform the existing method for over-determined and under-determined linear equation, as well as in the application of image processing.

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