An Inertial Three-Term Conjugate Gradient Projection Method With Applications

This paper introduces a robust inertial three-term projection method for solving monotone nonlinear equations. The proposed approach extends existing nonlinear conjugate gradient (CG) methods for unconstrained optimization with inexact line search by incorporating an inertial mechanism and a redesigned three-term search direction to enhance numerical efficiency. The proposed method guarantees that the search direction consistently satisfies the sufficient descent condition and maintains the trust region property. We demonstrate global convergence without requiring Lipschitz continuity and establish a linear convergence rate under some mild assumptions. Using some benchmark test problems, extensive numerical experiments demonstrate the excellent performance of the proposed algorithm. Furthermore, it showcases its practical applications in two key scientific fields: regularized decentralized logistic regression, a crucial model in data analysis, and image recovery, a prominent area in signal processing. The results demonstrate that the suggested approach is more efficient and effective in these applications.