Another hybrid approach for solving monotone operator equations and application to signal processing

Poom Kumam; Auwal Bala Abubakar; Abdulkarim Hassan Ibrahim; Hamza Umar Kura; Bancha Panyanak; Nuttapol Pakkaranang

doi:10.1002/mma.8285

Another hybrid approach for solving monotone operator equations and application to signal processing

Poom Kumam, Auwal Bala Abubakar, Abdulkarim Hassan Ibrahim, Hamza Umar Kura, Bancha Panyanak, Nuttapol Pakkaranang^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai-Yuan (DY)-like and Hestenes-Stiefel (HS)-like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

Original language	English
Pages (from-to)	7897-7922
Number of pages	26
Journal	Mathematical Methods in the Applied Sciences
Volume	45
Issue number	12
DOIs	https://doi.org/10.1002/mma.8285
Publication status	Published - Aug 2022
Externally published	Yes

Keywords

compressive sensing
global convergence
gradient method
l-norm minimization
projection method
signal reconstruction

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10.1002/mma.8285

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title = "Another hybrid approach for solving monotone operator equations and application to signal processing",

abstract = "This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai-Yuan (DY)-like and Hestenes-Stiefel (HS)-like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.",

keywords = "compressive sensing, global convergence, gradient method, l-norm minimization, projection method, signal reconstruction",

author = "Poom Kumam and Abubakar, {Auwal Bala} and Ibrahim, {Abdulkarim Hassan} and Kura, {Hamza Umar} and Bancha Panyanak and Nuttapol Pakkaranang",

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volume = "45",

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AU - Kumam, Poom

AU - Abubakar, Auwal Bala

AU - Ibrahim, Abdulkarim Hassan

AU - Kura, Hamza Umar

AU - Panyanak, Bancha

AU - Pakkaranang, Nuttapol

PY - 2022/8

Y1 - 2022/8

N2 - This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai-Yuan (DY)-like and Hestenes-Stiefel (HS)-like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

AB - This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai-Yuan (DY)-like and Hestenes-Stiefel (HS)-like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

KW - compressive sensing

KW - global convergence

KW - gradient method

KW - l-norm minimization

KW - projection method

KW - signal reconstruction

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SP - 7897

EP - 7922

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 12

ER -

Another hybrid approach for solving monotone operator equations and application to signal processing

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Keywords

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