An accelerated Bouligand–Landweber method based on projection and Nesterov acceleration for nonsmooth ill-posed problems

In this paper, we propose an accelerated Bouligand–Landweber method which is based on projection and Nesterov acceleration. This approach incorporates Nesterov acceleration technique into the Bouligand Landweber method whose step sizes are determined by projection. It is designed to solve nonsmooth ill-posed problems and to reduce the computational time. When the data is exact, we show the convergence result of the proposed method. When the data is contaminated by noise, we prove its regularization property by utilizing the concept of asymptotic stability. Moreover, some numerical experiments on nonsmooth inverse problems are performed to demonstrate the efficiency and the acceleration effect of the method.