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An efficient projection algorithm for solving convex constrained monotone operator equations and sparse signal reconstruction problems

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Abstract

We propose an efficient three-term projection method for solving convex-constrained nonlinear monotone equations, with applications to sparse signal reconstruction problems, in this paper. The proposed algorithm has three main appealing features; it is a new variant of BFGS modification; it satisfies the famous D–L conjugacy condition, and it satisfies the sufficient descent condition. The global convergence of the proposed algorithm is proven under some suitable conditions. Numerical results presented display the efficacy of the proposed algorithm in comparison with existing algorithms. Finally, the proposed algorithm is used to solve the sparse signal reconstruction problem.

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Acknowledgements

The second author acknowledges with thanks, the Nonlinear Dynamics and Mathematical Application Center, Kyungpook National University, Republic of Korea for providing excellent research facilities and the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University. The fourth author is grateful to the support of Bansomdejchaopraya Rajabhat University.

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Authors and Affiliations

  1. Department of Mathematics, Sule Lamido University, Kafin-Hausa, Jigawa State, Nigeria

    Muhammad Abdullahi

  2. Numerical Optimization Research Group, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano, Kano, Kano State, Nigeria

    Muhammad Abdullahi, Auwal Bala Abubakar & Abba Sulaiman

  3. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Ga-Rankuwa, Pretoria, 0204, South Africa

    Auwal Bala Abubakar

  4. Nonlinear Dynamics and Mathematical Application Center, Kyungpook National University, Daegu, Republic of Korea

    Auwal Bala Abubakar

  5. Department of Mathematics, Faculty of Science and Technology, Bansomdejchaopraya Rajabhat University, 1061 Isaraphab 15 Rd., Dhonburi, Bangkok, 10600, Thailand

    Porawee Chotpitayasunon

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

    Muhammad Abdullahi

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  1. Muhammad Abdullahi
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Correspondence to Porawee Chotpitayasunon.

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Abdullahi, M., Abubakar, A.B., Sulaiman, A. et al. 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

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