On a Scaled Symmetric Dai–Liao-Type Scheme for Constrained System of Nonlinear Equations with Applications

Kabiru Ahmed (), Mohammed Yusuf Waziri (), Salisu Murtala (), Abubakar Sani Halilu () and Jamilu Sabi’u ()
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Kabiru Ahmed: Bayero University
Mohammed Yusuf Waziri: Bayero University
Salisu Murtala: Bayero University
Abubakar Sani Halilu: Bayero University
Jamilu Sabi’u: Bayero University

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 2, No 9, 669-702

Abstract: Abstract In this paper, a new Dai–Liao (DL)-type projection algorithm is presented for large-dimension nonlinear monotone problems with signal reconstruction and image recovery applications. The inspiration behind the work comes from two of the open problems propounded by Andrei (Bull Malays Math Sci Soc 34(2):319–330, 2011) involving the optimal value for the DL nonnegative parameter and the best conjugacy condition as well as the fine attributes expressed by four-term methods for unconstrained optimization. Based on the eigenvalue study of a symmetric DL-type iteration matrix, another optimal choice of the DL parameter is obtained, which is incorporated in a five-term direction scheme. Combining this with the projection method, a new DL algorithm which converges globally is developed. To implement the algorithm, a derivative-free line search mechanism is employed. Also, by conducting some numerical experiments with the new scheme and some recent DL-type methods, the efficiency of the former in solving nonlinear monotone problems as well as the $$\ell _1-norm$$ ℓ 1 - n o r m regularized problems in compressed sensing is demonstrated.

Keywords: Nonlinear Monotone equations; Eigenvalues; Convergence rate; Convex constraint; Compressed sensing; 90C30; 90C26; 94A12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02281-6

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