A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

Poom Kumam; Auwal Bala Abubakar; Maulana Malik; Abdulkarim Hassan Ibrahim; Nuttapol Pakkaranang; Bancha Panyanak

doi:10.1016/j.cam.2023.115304

A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

Poom Kumam, Auwal Bala Abubakar, Maulana Malik, Abdulkarim Hassan Ibrahim, Nuttapol Pakkaranang^*, Bancha Panyanak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This article presents a new hybrid conjugate gradient (CG) algorithm for solving unconstrained optimization problem. The search direction is defined as a combination of Hestenes–Stiefel (HS) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) quasi-Newton direction. In addition, the search direction is descent and bounded. The global convergence of the algorithm is obtained under the Wolfe-type and Armijo-type line searches. Numerical experiments on some benchmark test problems is carried out to depict the efficiency and robustness of the hybrid algorithm. Furthermore, a practical application of the algorithm in motion control of robot manipulator and image restoration is provided.

Original language	English
Article number	115304
Journal	Journal of Computational and Applied Mathematics
Volume	433
DOIs	https://doi.org/10.1016/j.cam.2023.115304
Publication status	Published - 1 Dec 2023
Externally published	Yes

Keywords

Global convergence
Line search
Three-term conjugate gradient method
Unconstrained optimization

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10.1016/j.cam.2023.115304

Cite this

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title = "A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery",

abstract = "This article presents a new hybrid conjugate gradient (CG) algorithm for solving unconstrained optimization problem. The search direction is defined as a combination of Hestenes–Stiefel (HS) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) quasi-Newton direction. In addition, the search direction is descent and bounded. The global convergence of the algorithm is obtained under the Wolfe-type and Armijo-type line searches. Numerical experiments on some benchmark test problems is carried out to depict the efficiency and robustness of the hybrid algorithm. Furthermore, a practical application of the algorithm in motion control of robot manipulator and image restoration is provided.",

keywords = "Global convergence, Line search, Three-term conjugate gradient method, Unconstrained optimization",

author = "Poom Kumam and Abubakar, {Auwal Bala} and Maulana Malik and Ibrahim, {Abdulkarim Hassan} and Nuttapol Pakkaranang and Bancha Panyanak",

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T1 - A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

AU - Kumam, Poom

AU - Abubakar, Auwal Bala

AU - Malik, Maulana

AU - Ibrahim, Abdulkarim Hassan

AU - Pakkaranang, Nuttapol

AU - Panyanak, Bancha

PY - 2023/12/1

Y1 - 2023/12/1

N2 - This article presents a new hybrid conjugate gradient (CG) algorithm for solving unconstrained optimization problem. The search direction is defined as a combination of Hestenes–Stiefel (HS) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) quasi-Newton direction. In addition, the search direction is descent and bounded. The global convergence of the algorithm is obtained under the Wolfe-type and Armijo-type line searches. Numerical experiments on some benchmark test problems is carried out to depict the efficiency and robustness of the hybrid algorithm. Furthermore, a practical application of the algorithm in motion control of robot manipulator and image restoration is provided.

AB - This article presents a new hybrid conjugate gradient (CG) algorithm for solving unconstrained optimization problem. The search direction is defined as a combination of Hestenes–Stiefel (HS) and the Liu–Storey (LS) CG parameters and is close to the direction of the memoryless Broyden–Fletcher–Goldferb–Shanno (BFGS) quasi-Newton direction. In addition, the search direction is descent and bounded. The global convergence of the algorithm is obtained under the Wolfe-type and Armijo-type line searches. Numerical experiments on some benchmark test problems is carried out to depict the efficiency and robustness of the hybrid algorithm. Furthermore, a practical application of the algorithm in motion control of robot manipulator and image restoration is provided.

KW - Global convergence

KW - Line search

KW - Three-term conjugate gradient method

KW - Unconstrained optimization

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DO - 10.1016/j.cam.2023.115304

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JO - Journal of Computational and Applied Mathematics

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A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery

Abstract

Keywords

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