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An adaptive family of projection methods for constrained monotone nonlinear equations with applications

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  • Gao, Peiting
  • He, Chuanjiang
  • Liu, Yang

Abstract

An adaptive class of conjugate gradient methods is proposed in this paper, which all possess descent property under strong-wolfe line search. The adaptive parameter in the search direction is determined by minimizing the distance between relative matrix and self-scaling memoryless BFGS update by Oren in the Frobenius norm. Two formulas of the adaptive parameter are further obtained, which are presented as those given by Oren and Luenberger (1973/74) and respectively Oren and Spedicato (1976). By projection technology, two adaptive projection algorithms are developed for solving monotone nonlinear equations with convex constraints. Some numerical comparisons show that these two algorithms are efficient. Last, the proposed algorithms are used to recover a sparse signal from incomplete and contaminated sampling measurements; the results are promising.

Suggested Citation

  • Gao, Peiting & He, Chuanjiang & Liu, Yang, 2019. "An adaptive family of projection methods for constrained monotone nonlinear equations with applications," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 1-16.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:1-16
    DOI: 10.1016/j.amc.2019.03.064
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    References listed on IDEAS

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    1. Dai, Zhifeng & Chen, Xiaohong & Wen, Fenghua, 2015. "A modified Perry’s conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 378-386.
    2. XiaoLiang Dong & Hongwei Liu & Yubo He, 2015. "A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 225-241, April.
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    Cited by:

    1. Aliyu Yusuf & Nibron Haggai Manjak & Hassan Mohammad & Aliyu Ibrahim Kiri & Auwal Bala Abubakar, 2024. "A Solution Method for Nonlinear Monotone Equations via Hybrid Spectral Conjugate Gradient and Signal Recovery Problems," SN Operations Research Forum, Springer, vol. 5(2), pages 1-16, June.
    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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