两个充分下降的RMIL型共轭梯度法及图像去噪应用

doi:10.15960/j.cnki.issn.1007-6093.2026.02.006

Abstract

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

CLC Number:

O221.2

WU Xiaoyu, SHAO Hu, LIU Pengjie, ZHOU Jincheng. Two RMIL-type conjugate gradient methods with sufficient descent property and applications in image restoration[J]. Operations Research Transactions, 2026, 30(2): 79-92.

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

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