A modified Dai–Yuan method with restart mechanism for nonlinear system of equations with a signal recovery

Authors

  • A. S. Halilu
    Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, 22200 Terengganu, Malaysia
    Department of Mathematics, Sule Lamido University Kafin Hausa, Nigeria
    Numerical Optimization Research Group, Bayero University, Kano, Nigeria
    Mathematical Innovation and Applications Research Group, Sule Lamido University Kafin Hausa, Nigeria
  • M.A. Mohamed
    Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, 22200 Terengganu, Malaysia
  • I. A. R. Moghrabi
    Information Systems and Technology Department, Kuwait Technical College, Kuwait
    Department of Computer Science, College of Arts and Sciences, University of Central Asia, Naryn, Kyrgyz Republic
  • K. Ahmed
    Numerical Optimization Research Group, Bayero University, Kano, Nigeria
    Department of Mathematical Sciences, Bayero University, Kano, Nigeria
    Department of Mathematics, Federal University, Dutse, Nigeria
  • S. M. Ibrahim
    College of Applied and Health Sciences, A’Sharqiyah University, 400 Ibra, Sultanate of Oman
  • M. Y. Waziri
    Numerical Optimization Research Group, Bayero University, Kano, Nigeria
    Department of Mathematical Sciences, Bayero University, Kano, Nigeria
  • S. Murtala
    Numerical Optimization Research Group, Bayero University, Kano, Nigeria
    Information Systems and Technology Department, Kuwait Technical College, Kuwait
    Department of Mathematics, Federal University, Dutse, Nigeria
  • H. Abdullahi
    Department of Mathematics, Sule Lamido University Kafin Hausa, Nigeria
    Mathematical Innovation and Applications Research Group, Sule Lamido University Kafin Hausa, Nigeria
    Department of Mathematical Sciences, Bayero University, Kano, Nigeria
  • M. A. Jada
    Mathematical Innovation and Applications Research Group, Sule Lamido University Kafin Hausa, Nigeria
    Department of Mathematical Sciences, Bayero University, Kano, Nigeria

Keywords:

Conjugate gradient methods, Lipschitz condition, Signal reconstruction, Singular values

Abstract

The Dai--Yuan method is an important iterative scheme for solving unconstrained optimization problems, but it often requires exact or Wolfe-type line searches to satisfy descent or sufficient descent conditions. It may also perform poorly due to the jamming phenomenon. This paper presents a modified three-term Dai--Yuan method for solving constrained systems of nonlinear monotone equations. The search direction of the proposed method includes a nonnegative parameter whose value is determined through singular-value analysis of the iteration matrix. The method also incorporates a restart mechanism that ensures global convergence regardless of the line-search procedure used. Theoretical analysis establishes the global convergence and convergence rate of the proposed scheme under suitable assumptions. Numerical experiments on constrained nonlinear equations and sparse signal reconstruction demonstrate the efficiency of the method compared with related algorithms.

Dimensions

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Published

2026-06-09

How to Cite

A modified Dai–Yuan method with restart mechanism for nonlinear system of equations with a signal recovery. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3051. https://doi.org/10.46481/jnsps.2026.3051

Issue

Volume 8, Issue 3, August 2026 (In Progress)

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 A. S. Halilu, M.A. Mohamed, I. A. R. Moghrabi, K. Ahmed, S. M. Ibrahim, M. Y. Waziri, S. Murtala, H. Abdullahi, M. A. Jada (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

A modified Dai–Yuan method with restart mechanism for nonlinear system of equations with a signal recovery. (2026). Journal of the Nigerian Society of Physical Sciences, 8(3), 3051. https://doi.org/10.46481/jnsps.2026.3051

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