线性约束优化问题的快速Bregman投影法

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-05-31 DOI:10.1016/j.cam.2025.116792

Yu-Xin Ye , Jun-Feng Yin , Yu-Rui Jiang , Ze Wang

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引用次数: 0

摘要

针对线性约束优化问题，提出了一种快速的Bregman投影方法，即贪婪地利用残差生成一个加权超平面。在无噪声和有噪声两种情况下，建立并研究了该方法的收敛性理论。详细推导了该方法的线性收敛率及其上界，优于速写Bregman投影法。数值实验验证了该方法在迭代次数和CPU时间方面的有效性。

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A fast Bregman projection method for linearly constrained optimization problems

A fast Bregman projection method is proposed for the solution of linearly constrained optimization problems by greedily making use of the residual to generate a weighted hyperplane. The convergence theories of the proposed method are established and studied under both noise-free and noisy cases. The linear convergence rate and its upper bound are derived in details, which is better than that of the sketched Bregman projection method. Numerical experiments verify the efficiency of the proposed method in terms of the number of iterations and CPU time.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.