THE GENERALIZED FORWARD-BACKWARD SPLITTING METHOD FOR THE MINIMIZATION OF THE SUM OF TWO FUNCTIONS IN BANACH SPACES

We propose a convergence analysis of the generalized forward-backward splitting iterative procedure for the minimization of the sum of two functions in Banach spaces. The generalized forward-backward splitting method is applied to the minimization of functionals of the Tikhonov type with semi-norm regularization. We also investigate the perturbed forward-backward splitting method and prove its stability.