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FR type methods for systems of large-scale nonlinear monotone equations

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  • Papp, Zoltan
  • Rapajić, Sanja

Abstract

A large class of iterative methods for solving nonlinear monotone systems is developed in recent years. In this paper we propose some new FR type directions in the frame of algorithm which is a combination of conjugate gradient approach and hyperplane projection technique. Derivative-free, function-value-based line search combined with projection procedure is used for globalization strategy. Numerical performances of methods with different search directions are compared.

Suggested Citation

  • Papp, Zoltan & Rapajić, Sanja, 2015. "FR type methods for systems of large-scale nonlinear monotone equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 816-823.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:816-823
    DOI: 10.1016/j.amc.2015.08.002
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Auwal Bala Abubakar & Poom Kumam & Hassan Mohammad & Aliyu Muhammed Awwal & Kanokwan Sitthithakerngkiet, 2019. "A Modified Fletcher–Reeves Conjugate Gradient Method for Monotone Nonlinear Equations with Some Applications," Mathematics, MDPI, vol. 7(8), pages 1-25, August.
    2. Xiaoyu Wu & Hu Shao & Pengjie Liu & Yue Zhuo, 2023. "An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1130-1155, September.

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