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

• Published in: Journal of applied mathematics & computing Vol. 70; no. 4; pp. 3879 - 3915
• Main Authors: Salihu, Sadiq Bashir, Halilu, Abubakar Sani, Abdullahi, Muhammad, Ahmed, Kabiru, Mehta, Pramod, Murtala, Salisu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Conjugate gradient method; Convergence; Integration; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Nonlinear equations; Numerical analysis; Original Research; Searching; Signal processing; Signal reconstruction; Theory of Computation; Monotone equation; Global convergence; Spectral conjugate; 65K05; 90C52; 94A08; 90C56; Signal processing; Sufficient descent
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-024-02121-4

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.