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

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2021-01-01 DOI:10.3934/naco.2021044

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

引用次数: 10

Abstract

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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非线性系统的改进Dai-Yuan迭代格式及其应用

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.