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An improved spectral conjugate gradient projection method for monotone nonlinear equations with application

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Abstract

In this paper, we propose an enhanced spectral conjugate gradient (CG) projection method for solving monotone nonlinear equations with application in signal processing. The derivation of the CG parameter involves a combination of the quasi-Newton and the CG search directions, respectively. This integration aims to harness the efficiency of the quasi-Newton direction and the global convergence properties of the CG method, resulting in a more versatile and efficient algorithm. The search direction ensures sufficient descent without relying on any line search, and the global convergence of the proposed method is established under certain conditions. Numerical experiments have been conducted to evaluate the effectiveness of the proposed method. Finally, the proposed method has been applied to address the problems arising in signal reconstruction.

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References

  1. Abbass, G., Chen, H., Abdullahi, M., Baba, M.A., Musa, S.: A projection method for solving monotone nonlinear equations with application. Phys. Scr. 98(11), 115250 (2023)

    Article  Google Scholar 

  2. Abdullahi, M., Abubakar, A.B., Feng, Y., Liu, J.: Comment on: A derivative-free iterative method for nonlinear monotone equations with convex constraints. Numer. Algorithms (2023). https://doi.org/10.1007/s11075-023-01546-5

    Article  MathSciNet  Google Scholar 

  3. Abdullahi, M., Abubakar, A.B., Muangchoo, K.: Modified three-term derivative-free projection method for solving nonlinear monotone equations with application. Numer. Algorithms (2023). https://doi.org/10.1007/s11075-023-01616-8

    Article  Google Scholar 

  4. Abdullahi, M., Abubakar, A.B., Salihu, S.B.: Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems. RAIRO-Operations Res. 57(5), 2561–2584 (2023)

    Article  MathSciNet  Google Scholar 

  5. Abdullahi, M., Abubakar, A.B., Sulaiman, A., Chotpitayasunon, P.: An efficient projection algorithm for solving convex constrained monotone operator equations and sparse signal reconstruction problems. J. Anal. (2024). https://doi.org/10.1007/s41478-024-00757-w

    Article  Google Scholar 

  6. Abdullahi, M., Halilu, A.S., Awwal, A.M., Pakkaranang, N.: On efficient matrix-free method via quasi-newton approach for solving system of nonlinear equations. Adv. Theory Nonlinear Anal. its Appl. 5(4), 568–579 (2021)

    Google Scholar 

  7. Abubakar, A.B., Kumam, P., Awwal, A.M.: Global convergence via descent modified three-term conjugate gradient projection algorithm with applications to signal recovery. Results Appl. Math. 4, 100069 (2019)

    Article  MathSciNet  Google Scholar 

  8. Abubakar, A.B., Kumam, P., Mohammad, H., Awwal, A.M., Sitthithakerngkiet, K.: A modified fletcher-reeves conjugate gradient method for monotone nonlinear equations with some applications. Mathematics 7(8), 745 (2019)

    Article  Google Scholar 

  9. Abubakar, A.B., Rilwan, J., Yimer, S.E., Ibrahim, A.H., Ahmed, I.: Spectral three-term conjugate descent method for solving nonlinear monotone equations with convex constraints. Thai J. Math. 18(1), 501–517 (2020)

    MathSciNet  Google Scholar 

  10. Awwal, A.M., Kumam, P., Abubakar, A.B.: A modified conjugate gradient method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 145, 507–520 (2019)

    Article  MathSciNet  Google Scholar 

  11. Awwal, A.M., Kumam, P., Abubakar, A.B.: A modified conjugate gradient method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 145, 507–520 (2019)

    Article  MathSciNet  Google Scholar 

  12. Davidon, W.C.: Convergence of variable metric methods. J. Soc. Ind. Appl. Math. 7(1), 46–63 (1959)

    Google Scholar 

  13. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)

    Article  MathSciNet  Google Scholar 

  14. Figueiredo, M.A.T., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. sel. top. sign. proc. 1(4), 586–597 (2007)

    Article  Google Scholar 

  15. Halilu, A.S., Majumder, A., Waziri, M.Y., Abdullahi, H.: Double direction and step length method for solving system of nonlinear equations. Eur. J. Mol. Clin. Med. 7(7), 3899–3913 (2020)

    Google Scholar 

  16. Halilu, A.S., Majumder, A., Waziri, M.Y., Ahmed, K., Murtala, S.: Three-term hager-zhang projection method for monotone nonlinear equations. Vietnam J. Math. (2023). https://doi.org/10.1007/s10013-023-00639-x

    Article  Google Scholar 

  17. Halilu, A.S., Majumder, A., Waziri, M.Y., Awwal, A.M., Ahmed, K.: On solving double direction methods for convex constrained monotone nonlinear equations with image restoration. Comput. Appl. Math. 40, 1–27 (2021)

    Article  MathSciNet  Google Scholar 

  18. Halilu, A.S., Waziri, M.Y.: A transformed double step length method for solving large-scale systems of nonlinear equations. J. Numer. Math. Stoch. 9(1), 20–23 (2017)

    MathSciNet  Google Scholar 

  19. Kabiru, A., Waziri, M.Y., Halilu, A.S., Salisu, M.: Sparse signal reconstruction via hager–zhang-type schemes for constrained system of nonlinear equations. Optimization (2023). https://doi.org/10.1080/02331934.2023.2187255

    Article  Google Scholar 

  20. Liu, J., Feng, Y.: A derivative-free iterative method for nonlinear monotone equations with convex constraints. Numerical Algorithms 82, 245–262 (2019)

    Article  MathSciNet  Google Scholar 

  21. Liu, J., Feng, Y.: A derivative-free iterative method for nonlinear monotone equations with convex constraints. Numerical Algorithms 82, 245–262 (2019)

    Article  MathSciNet  Google Scholar 

  22. Liu, J., Li, S.: A projection method for convex constrained monotone nonlinear equations with applications. Comput. Math. Appl. 70(10), 2442–2453 (2015)

    Article  MathSciNet  Google Scholar 

  23. Solodov, M.V., Svaiter, B.F.: A globally convergent inexact Newton method for systems of monotone equations. In: Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, pages 355–369. Springer, (1998)

  24. Wang, C., Wang, Y., Xu, C.: A projection method for a system of nonlinear monotone equations with convex constraints. Math. Methods Oper. Res. 66, 33–46 (2007)

    Article  MathSciNet  Google Scholar 

  25. Waziri, M.Y., Ahmed, K., Sabiu, J., Halilu, A.S.: Enhanced dai-liao conjugate gradient methods for systems of monotone nonlinear equations. SeMA J. 78, 15–51 (2021)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The first author intends to convey his appreciation to Professor Peng Jun for the guidance, counsel, and assistance extended during this research. The third author wishes to express gratitude to the Department of Mathematics and Applied Mathematics, Central South University, Changsha, Hunan, China.

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Authors and Affiliations

  1. School of Mathematics and Statistics, HNP-LAMA Central South University Changsha, Hunan, 410083, China

    Sadiq Bashir Salihu & Muhammad Abdullahi

  2. Department of Mathematics, Sule Lamido University, Kafin-Hausa, Nigeria

    Abubakar Sani Halilu & Muhammad Abdullahi

  3. Department of Mathematics, School of Science, Jigawa State College of Education Gumel, Gumel, Nigeria

    Sadiq Bashir Salihu

  4. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Kabiru Ahmed

  5. Department of Mathematics, Federal University Dutse, Jigawa, Nigeria

    Salisu Murtala

  6. Department of Mathematics, Mewar University India, NH-48 Gangrar chittorgarh, Rajasthan, 312901, India

    Sadiq Bashir Salihu & Pramod Mehta

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  1. Sadiq Bashir Salihu
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  2. Abubakar Sani Halilu
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  3. Muhammad Abdullahi
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  4. Kabiru Ahmed
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  5. Pramod Mehta
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  6. Salisu Murtala
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Correspondence to Sadiq Bashir Salihu.

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Salihu, S.B., Halilu, A.S., Abdullahi, M. et al. An improved spectral conjugate gradient projection method for monotone nonlinear equations with application. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02121-4

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  • DOI: https://doi.org/10.1007/s12190-024-02121-4

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