A hybrid approach to conjugate gradient algorithms for nonlinear systems of equations with applications in signal restoration

• DOI: 10.3934/math.20241717
• Publication Date: 2024-12-28T10:28:32Z
• Authors: Xuejie Ma; Songhua Wang
• Keywords: Conjugate; SIGNAL (programming language)

<p>This paper proposes a novel hybrid PRP-HS-LS-type conjugate gradient algorithm for solving constrained nonlinear systems of equations. The proposed presents several significant advancements and key features: (i) the parameter is constructed by utilizing technique; (ii) search direction, designed with parameter, possesses sufficient descent trust region properties without need line mechanism; (iii) global convergence rigorously established under general assumptions, notably requirement Lipschitz continuity condition; (vi) numerical experiments demonstrate algorithm's efficiency, particularly in large-scale equations addressing sparse signal restoration problem.</p>