一个具有充分下降性的谱共轭梯度法及其在图像恢复中的应用  

A SPECTRAL CONJUGATE GRADIENT METHOD WITH SUFFICIENT DESCENT PROPERTY AND ITS APPLICATION IN IMAGE RESTORATION

作　　者：李怡昕 李春光 张宗宁 杨威 Li Yixin;Li Chunguang;Zhang Zongning;Yang Wei(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021;Department of Basic Courses,Zhengzhou University of Science and Technology,Zhengzhou 45006)

机构地区：[1]北方民族大学数学与信息科学学院,银川750021 [2]郑州科技学院基础部,郑州450064

出　　处：《高等学校计算数学学报》2023年第4期371-384,共14页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11761005).

摘　　要：1引言.共轭梯度法是求解无约束优化问题min f(x),x ∈ R^(n),(1)的有效方法之一。其迭代点列通常由以下公式产生。In this paper,a new spectral conjugate gradient method is proposed by using the improved conjugate parameter of PRP conjugate gradient method and designing a new spectral parameter for solving large scale unconstrained optimiza-tion problems.This method satisfies the sufficient descent property independent of any line search.The global convergence of the new algorithm can be proved under the conditions of conventional assumptions if the strong Wolfe inexact line search is adopted.Large-scale numerical comparisons and image recovery tests with other algorithms show that this new algorithm has good numerical performance and good image recovery effect.

关 键 词：共轭梯度法 无约束优化问题 充分下降性 迭代点 图像恢复 

分 类 号：O224[理学—运筹学与控制论]