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A projection method for a system of nonlinear monotone equations with convex constraints

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  • Chuanwei Wang
  • Yiju Wang
  • Chuanliang Xu

Abstract

In this paper, we propose a projection method for solving a system of nonlinear monotone equations with convex constraints. Under standard assumptions, we show the global convergence and the linear convergence rate of the proposed algorithm. Preliminary numerical experiments show that this method is efficient and promising. Copyright Springer-Verlag 2007

Suggested Citation

  • Chuanwei Wang & Yiju Wang & Chuanliang Xu, 2007. "A projection method for a system of nonlinear monotone equations with convex constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(1), pages 33-46, August.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:1:p:33-46
    DOI: 10.1007/s00186-006-0140-y
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    References listed on IDEAS

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    1. X. J. Tong & L. Qi, 2004. "On the Convergence of a Trust-Region Method for Solving Constrained Nonlinear Equations with Degenerate Solutions," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 187-211, October.
    2. G. Zhou & K. C. Toh, 2005. "Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 205-221, April.
    3. Y. J. Wang & N. H. Xiu & J. Z. Zhang, 2003. "Modified Extragradient Method for Variational Inequalities and Verification of Solution Existence," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 167-183, October.
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    Cited by:

    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Wang, John & Yan, Ruiliang & Hollister, Kimberly & Zhu, Dan, 2008. "A historic review of management science research in China," Omega, Elsevier, vol. 36(6), pages 919-932, December.
    3. 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.
    4. Gonglin Yuan & Xiaoliang Wang & Zhou Sheng, 2020. "The Projection Technique for Two Open Problems of Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 590-619, August.
    5. Auwal Bala Abubakar & Poom Kumam & Aliyu Muhammed Awwal & Phatiphat Thounthong, 2019. "A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems," Mathematics, MDPI, vol. 7(8), pages 1-24, August.
    6. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.

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