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Solving nonlinear monotone operator equations via modified SR1 update

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Abstract

In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms were established under suitable assumptions on the operator under consideration. In addition, numerical experiments were conducted on some benchmark test problems to depict the efficiency and competitiveness of the algorithms compared with existing algorithms. From the results of the experiments, we can conclude that the proposed algorithms are more efficient and robust.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.

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Correspondence to Poom Kumam.

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Abubakar, A.B., Sabi’u, J., Kumam, P. et al. Solving nonlinear monotone operator equations via modified SR1 update. J. Appl. Math. Comput. 67, 343–373 (2021). https://doi.org/10.1007/s12190-020-01461-1

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  • DOI: https://doi.org/10.1007/s12190-020-01461-1

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