An inertial conjugate gradient projection method for large-scale nonlinear equations and its application in the image restoration problems

Based on the acceleration effect of the inertial extrapolation technique on the convergence of iterative sequences, the number of algorithms incorporating this technique has gradually increased in recent years. Currently, there is a relative paucity of studies focusing on the Polak-Ribière-Polyak (PRP) conjugate gradient algorithm that integrate the inertial extrapolation technique. In this article, we introduce an inertial three-term PRP conjugate gradient projection method by incorporating an inertial extrapolation step into the three-term PRP algorithm, where the search direction exhibits sufficient descent and trust region characteristics. The search rule employs a derivative-free technique. Under suitable hypotheses, the proposed algorithm demonstrates global convergence. Numerical results indicate the superiority and competitiveness of this innovative method. Furthermore, its effectiveness in addressing image restoration problems underscores the practicality of this algorithm.