An accelerated sequential subspace optimization method based on homotopy perturbation iteration for nonlinear ill-posed problems

Abstract

Homotopy perturbation iteration is an effective and fast method for solving nonlinear ill-posed problems. It only needs approximately half the computation time of Landweber iteration to reach the similar recovery precision. In this paper, a Nesterov-type accelerated sequential subspace optimization method based on homotopy perturbation iteration is proposed for solving nonlinear inverse problems. The convergence analysis is provided under the general assumptions for iterative regularization methods. The numerical experiments on inverse potential problem indicate that the proposed method dramatically reduces the total number of iterations and time consumption to obtain satisfying approximations, especially for the problems with costly solution of forward calculation.