A conjugate gradient algorithmic framework for unconstrained optimization with applications: Convergence and rate analyses

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2026-02-01 Epub Date: 2025-10-09 DOI:10.1016/j.apnum.2025.10.006

Feng Shao , Hu Shao , Bin Wu , Haijun Wang , Pengjie Liu , Meixing Liu

引用次数: 0

Abstract

In this paper, we aim to develop a general conjugate gradient (CG) algorithmic framework for solving unconstrained optimization problems. Additionally, we employ different hybrid techniques to derive two hybrid conjugate parameters, which are then integrated into the algorithmic framework to develop two effective hybrid CG methods. Under common assumptions, we establish the global convergence of the proposed framework without any convexity assumption. Furthermore, we reveal the convergence rate of the framework under the uniformly convex condition. Preliminary numerical experiment results, including applications to unconstrained optimization and image restoration problems, are presented to explicitly illustrate the performance of the proposed methods in comparison with several existing methods.

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无约束优化的共轭梯度算法框架及其应用：收敛性和速率分析

在本文中，我们的目标是建立一个通用的共轭梯度（CG）算法框架来解决无约束优化问题。此外，我们采用不同的混合技术来推导两个混合共轭参数，然后将其集成到算法框架中，以开发两种有效的混合CG方法。在一般假设下，我们建立了该框架的全局收敛性，而不需要任何凸性假设。进一步给出了该框架在一致凸条件下的收敛速度。初步的数值实验结果，包括在无约束优化和图像恢复问题上的应用，明确地说明了所提方法与几种现有方法的性能。

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.