An improved LS-RMIL-type conjugate gradient projection algorithm for systems of nonlinear equations and impulse noise image restoration

• Published in: AIMS mathematics Vol. 10; no. 6; pp. 13640 - 13663
• Main Authors: Xia, Yan, Ma, Xuejie, Li, and Dandan
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.06.2025
• Subjects: conjugate gradient projection method; global convergence; impulse noise image restoration; systems of nonlinear equations
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2025614

This paper proposes an improved LS-RMIL-type conjugate gradient projection algorithm designed for solving systems of nonlinear equations with convex constraints. The algorithm introduces a search direction that maintains sufficient descent and trust-region properties independent of the line search approach. It operates under relatively mild conditions, requiring only continuity and monotonicity of nonlinear equations, thus avoiding the need for stronger assumptions such as Lipschitz continuity. The global convergence of the algorithm is established under these relaxed conditions. Furthermore, numerical experiments demonstrate that the algorithm exhibits superior efficiency and stability, particularly in solving large-scale nonlinear systems and in applications such as impulse noise image restoration, outperforming existing methods.