An inertial three-term hybrid CG-based projection method for constrained nonlinear pseudo-monotone equations with applications

Abstract

In this work, we first take some modifications to the three-term conjugate gradient (CG) search direction proposed by Liu et al. [Applied Numerical Mathematics, 2022,175: 98-107], and the new search direction satisfies the sufficient descent and trust region properties which is independent of any line search. Then, combining with the inertial extrapolation step-length and hyperplane projection technique, we propose an inertial three-term hybrid CG-based projection method to solve nonlinear pseudo-monotone equations with convex constraints. The global convergence of our proposed method is analyzed and established without the Lipschitz continuity. Some numerical experiments are executed on the standard constrained nonlinear equations and their corresponding performance profiles are illustrated, which show that our proposed method is feasible and effective. Finally, our proposed method is extended to restore the blurred images contaminated by the Gaussian noise.