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An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications

Author

Listed:
  • Dandan Li

    (School of Artificial Intelligence, Guangzhou Huashang College, Guangzhou 511300, China)

  • Yong Li

    (School of Mathematics, Physics and Statistics, Baise University, Baise 533099, China)

  • Songhua Wang

    (School of Mathematics, Physics and Statistics, Baise University, Baise 533099, China)

Abstract

This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search direction inherently ensures sufficient descent and trust-region properties, eliminating the need for line search formulas; (iii) Global convergence is established without the necessity of the Lipschitz continuity condition. Benchmark problem numerical results illustrate the proposed algorithm’s effectiveness and competitiveness relative to other three-term algorithms. Additionally, the algorithm is extended to effectively address the image denoising problem.

Suggested Citation

  • Dandan Li & Yong Li & Songhua Wang, 2024. "An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications," Mathematics, MDPI, vol. 12(16), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2556-:d:1459048
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    References listed on IDEAS

    as
    1. Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    2. Najib Ullah & Abdullah Shah & Jamilu Sabi’u & Xiangmin Jiao & Aliyu Muhammed Awwal & Nuttapol Pakkaranang & Said Karim Shah & Bancha Panyanak, 2023. "A One-Parameter Memoryless DFP Algorithm for Solving System of Monotone Nonlinear Equations with Application in Image Processing," Mathematics, MDPI, vol. 11(5), pages 1-26, March.
    3. Eltiyeb Ali & Salem Mahdi, 2023. "Adaptive Hybrid Mixed Two-Point Step Size Gradient Algorithm for Solving Non-Linear Systems," Mathematics, MDPI, vol. 11(9), pages 1-35, April.
    Full references (including those not matched with items on IDEAS)

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