A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing

Najib Ullah, Abdullah Shah, Jamilu Sabi’u, Xiangmin Jiao, Aliyu Muhammed Awwal, Nuttapol Pakkaranang (), Said Karim Shah and Bancha Panyanak
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Najib Ullah: Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad 45550, Pakistan
Abdullah Shah: Department of Mathematics, College of Computing and Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Jamilu Sabi’u: Department of Mathematics, Yusuf Maitama Sule University, Kano 700282, Nigeria
Xiangmin Jiao: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York, NY 11794, USA
Aliyu Muhammed Awwal: Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe 760214, Nigeria
Nuttapol Pakkaranang: Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
Said Karim Shah: Department of Physics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
Bancha Panyanak: Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2023, vol. 11, issue 5, 1-26

Abstract: In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.

Keywords: one-parameter scaling; memoryless DFP algorithm; measure function; convex constraints; image restoration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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