A fast two-point gradient algorithm based on sequential subspace optimization method for nonlinear ill-posed problems

In this paper, we propose a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. The key idea, in contrast to the standard two-point gradient method, is to use multiple search directions in each iteration without extra computation, and to get the step size by metric projection. Moreover, a modified discrete backtracking search algorithm is proposed to select the combination parameters in the accelerated two-point gradient method. Under the basic assumptions for iterative regularization methods, we establish the convergence results of the method in the noise-free case. Furthermore, stability and regularity are presented when the algorithm terminated by the discrepancy principle for the case of noisy data. Finally, some numerical simulations are presented, which exhibit that the proposed method leads to a significant reduction of the iteration numbers and the overall computational time.