A generalized hybrid CGPM-based algorithm for solving large-scale convex constrained equations with applications to image restoration

In this paper, by improving a line search criterion to yield steplength, and designing a hybrid conjugate parameter to construct sufficient descent direction, we propose a generalized hybrid conjugate gradient projection method for solving large-scale monotone nonlinear equations with convex constraints. For the proposed method, we prove its global convergence under some mild conditions, and study its convergence rate. Numerical comparisons with two existing methods show that our method is promising for solving large-scale nonlinear constrained equations. Furthermore, the experiment results of dealing with image restoration problems also verify that the proposed method is effective.