1. Department of Mathematics, Harbin Institute of Technology , Harbin , P.R. China guanweibo0451@163.com;3. School of Mathematical Sciences , Harbin Normal University , Harbin , P.R. China
Abstract:
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.