A new conjugate gradient method with a restart direction and its application in image restoration

Yixin Li; Chunguang Li; Wei Yang; Wensheng Zhang; Yixin Li; Chunguang Li; Wei Yang; Wensheng Zhang

doi:10.3934/math.20231475

AIMS Mathematics

2023, Volume 8, Issue 12: 28791-28807. doi: 10.3934/math.20231475

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Research article

A new conjugate gradient method with a restart direction and its application in image restoration

School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

Received: 31 August 2023 Revised: 10 October 2023 Accepted: 15 October 2023 Published: 23 October 2023
MSC : 65K10, 68U10, 90C06

We established a new conjugate gradient method with an efficient restart direction for solving large scale unconstrained optimization problems. The modified method was proposed under the Polak-Ribière-Polyak conjugate gradient method. Under the strong Wolfe line search, the search direction of the new method was sufficiently descent and its global convergence property could be proved. Compared with other methods having good numerical performances, numerical experiments and image restorations showed that the modified method was more effective.
- unconstrained optimization,
- conjugate gradient method,
- strong Wolfe line search,
- global convergence,
- numerical experiment,
- image restoration
Citation: Yixin Li, Chunguang Li, Wei Yang, Wensheng Zhang. A new conjugate gradient method with a restart direction and its application in image restoration[J]. AIMS Mathematics, 2023, 8(12): 28791-28807. doi: 10.3934/math.20231475

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Abstract

We established a new conjugate gradient method with an efficient restart direction for solving large scale unconstrained optimization problems. The modified method was proposed under the Polak-Ribière-Polyak conjugate gradient method. Under the strong Wolfe line search, the search direction of the new method was sufficiently descent and its global convergence property could be proved. Compared with other methods having good numerical performances, numerical experiments and image restorations showed that the modified method was more effective.

References

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