A sufficient descent hybrid conjugate gradient method without line search consideration and application

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Nasiru Salihu, P. Kumam, Sulaiman Mohammed Ibrahim, Huzaifa Aliyu Babando
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引用次数: 0

Abstract

PurposePrevious RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.Design/methodology/approachThe conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.FindingsNumerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.Originality/valueThe strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.
无需考虑线搜索的充分下降混合共轭梯度法及其应用
目的以往文献中提出的共轭梯度法的 RMIL 版本在沃尔夫线搜索条件下表现出充分的下降性,但其全局收敛性取决于某些限制条件。为了减轻这些假设,我们提出了一种基于共轭条件的混合共轭梯度法。设计/方法/途径共轭梯度(CG)方法通过使用 RMIL 和 KMD CG 方法的凸组合,战略性地交替使用这两种方法,从而减轻了它们各自的弱点。在不考虑线性搜索的情况下,对混合方法进行的理论分析表明了其充分下降特性。通过对充分下降特性的理论理解,可以消除以前对 RMIL CG 方法的全局收敛结果施加的限制。研究结果使用结合了 RMIL 和 KMD CG 方法的混合策略进行的数值实验表明,与单独使用的每种方法相比,混合方法的性能更优越,甚至优于某些最新版本的 RMIL 方法。原创性/价值通过混合技术证明 RMIL CG 的充分下降特性和收敛结果而不考虑线搜索的策略,在以前的文献中还没有探索过。此外,基于搜索方向规范的假设,组合中涉及的两种 CG 方案表现出相似的充分下降结构。
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
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
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