An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-26 DOI:10.1016/j.apnum.2024.06.020

Zibo Chen , Hu Shao , Pengjie Liu , Guoxin Li , Xianglin Rong

引用次数: 0

Abstract

In this study, we introduce a novel hybrid conjugate gradient method with an adaptive strategy called asHCG method. The asHCG method exhibits the following characteristics. (i) Its search direction guarantees sufficient descent property without dependence on any line search. (ii) It possesses strong convergence for the uniformly convex function using a weak Wolfe line search, and under the same line search, it achieves global convergence for the general function. (iii) Employing the Armijo line search, it provides an approximate guarantee for worst-case complexity for the uniformly convex function. The numerical results demonstrate promising and encouraging performances in both unconstrained optimization problems and image restoration problems.

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具有自适应策略的高效混合共轭梯度法及其在图像复原问题中的应用

在本研究中，我们介绍了一种新颖的混合共轭梯度法，该方法采用自适应策略，称为 asHCG 方法。asHCG 方法具有以下特点。(i) 其搜索方向保证了充分下降特性，而不依赖于任何线性搜索。(ii) 对均匀凸函数采用弱沃尔夫线性搜索，具有很强的收敛性；对一般函数采用相同的线性搜索，可实现全局收敛。(iii) 利用 Armijo 行搜索，它为均匀凸函数的最坏情况复杂度提供了近似保证。数值结果表明，该方法在无约束优化问题和图像复原问题上都有令人鼓舞的良好表现。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.