An accelerated conjugate gradient method with adaptive two-parameter with applications in image restoration

This paper proposes an adaptive two-parameter accelerated conjugate gradient method, which satisfies the sufficient descent condition in the search direction. The Powell restart strategy is designed in the algorithm to improve its numerical performance. Our proposed method does not add extra computational effort compared to other methods. Furthermore, under general assumptions, we demonstrate the global convergence of our proposed method under the Wolfe line search. Finally, we compare with other methods on the unconstrained optimization and image restoration problems. Numerical experiments are presented to show that our proposed method is feasible.