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A modified Dai–Liao conjugate gradient method for solving unconstrained optimization and image restoration problems

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Abstract

In this paper, a new conjugacy condition is established to solve unconstrained optimization problems based on a new quasi-Newton equation. We present a modified Dai–Liao conjugate gradient method to solve unconstrained optimization problems with a new value of the parameter t based on the new conjugacy condition. The presented algorithm has the following properties: (i) the modified Dai–Liao conjugate gradient method considers both the gradient and function value information. (ii) The global convergence is achieved for the modified Dai–Liao conjugate gradient method under some suitable assumptions. (iii) Numerical experiments on unconstrained optimization problems and image restoration problems are conducted, and the numerical results show that our method is efficient.

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Correspondence to Gonglin Yuan.

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This work was supported by the National Natural Science Foundation of China (Grant No. 11661009), the High Level Innovation Teams and Excellent Scholars Program in Guangxi institutions of higher education (Grant No. [2019]52), the Guangxi Natural Science Key Fund (No. 2017GXNSFDA198046), and the Special Funds for Local Science and Technology Development Guided by the Central Government (No. ZY20198003)

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Lu, J., Yuan, G. & Wang, Z. A modified Dai–Liao conjugate gradient method for solving unconstrained optimization and image restoration problems. J. Appl. Math. Comput. 68, 681–703 (2022). https://doi.org/10.1007/s12190-021-01548-3

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