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运筹学学报 >

2026 , Vol. 30 >Issue 2: 79 - 92

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2026.02.006

两个充分下降的RMIL型共轭梯度法及图像去噪应用

  • 吴晓宇 ,
  • 邵虎 ,
  • 刘鹏杰 ,
  • 周金诚
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  • 中国矿业大学数学学院, 江苏徐州 221116

收稿日期: 2023-01-18

  网络出版日期: 2026-06-12

基金资助

国家自然科学基金 (Nos. 72471227,72071202), 江苏省研究生科研与实践创新计划项目 (No. KYCX25_2857), 中国矿业大学研究生创新计划项目 (No. 2025WLKXJ145)

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Two RMIL-type conjugate gradient methods with sufficient descent property and applications in image restoration

  • WU Xiaoyu ,
  • SHAO Hu ,
  • LIU Pengjie ,
  • ZHOU Jincheng
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  • School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China

Received date: 2023-01-18

  Online published: 2026-06-12

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摘要

共轭梯度法因其低存储、迭代简单等优点,广泛应用于求解大规模无约束优化问题。本文基于Rivaie-Mustafa-Ismail-Leong (RMIL)共轭参数,提出两个拓展的RMIL型共轭参数,并建立相应的共轭梯度算法。在强Wolfe非精确线搜索下,证明第一个算法产生的搜索方向满足充分下降性,并给出其全局收敛性证明。第二个算法不依赖任何线搜索,搜索方向有充分下降性;利用标准Wolfe线搜索产生步长,得到算法的全局收敛性。为测试两算法的数值效果,将其应用于求解无约束优化数值算例和图像去噪问题。与其他算法对比,本文结果表明两个新算法是有效的。

关键词： 无约束优化; 共轭梯度法; 全局收敛性; 图像去噪

本文引用格式

吴晓宇 , 邵虎 , 刘鹏杰 , 周金诚 . 两个充分下降的RMIL型共轭梯度法及图像去噪应用[J]. 运筹学学报, 2026 , 30(2) : 79 -92 . DOI: 10.15960/j.cnki.issn.1007-6093.2026.02.006

Abstract

The conjugate gradient method possesses the advantages of lower storage requirement and simplicity to iterate, therefore it has been widely used for solving the large-scale optimization problems. Based on the Rivaie-Mustafa-Ismail-Leong (RMIL) conjugate coefficient, we propose two extended RMIL-type coefficients and establish the corresponding conjugate gradient algorithms for solving unconstrained optimization problems. Under the strong Wolfe line search, we prove that the search direction sequence generated by the first algorithm satisfies the descent property. The global convergence property is established under the normal assumptions. The descending property of the second algorithm is independent of any line search condition. By using the standard Wolfe line search, the global convergence of the second algorithm is obtained. To test the numerical effects of two proposed algorithms, we apply them to solve unconstrained optimization problems and restore the blurred images affected by impulse noise. Compared with some existing conjugate gradient methods, experimental results show that the two proposed algorithms are promising.

Key words： unconstrained optimization; conjugate gradient method; global convergence; image restoration

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