非线性系统的改进Dai-Yuan迭代格式及其应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/naco.2021044

M. Waziri, K. Ahmed, A. Halilu, Aliyu Mohammed Awwal

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引用次数: 10

摘要

利用薛等人的谱代元法思想。参考文献[j] . system. 101(12)2984-2990(2018)]和用于非光滑优化的改进Hager-Zhang格式的方法[PLos ONE 11(10): e0164289(2016)]，我们开发了凸约束非线性单调系统的Dai-Yuan型迭代格式。该方案的算法是将其搜索方向与投影法相结合得到的[Kluwer Academic Publishers, pp. 355-369(1998)]。新方案的一个特性是无导数，这使得它非常适合求解非光滑问题。此外，我们通过将该方法的性能与最近的有效方法进行比较，证明了该方法在图像去模糊问题中的应用。通过采用温和的假设，确定了该方法的全局收敛性，数值实验结果表明，该方法与目前的一些迭代方法相比具有较好的收敛性。

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Modified Dai-Yuan iterative scheme for Nonlinear Systems and its Application

By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.