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The Generalized Forward-Backward Splitting Method for the Minimization of the Sum of Two Functions in Banach Spaces |
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| Authors: | Wei-Bo Guan Wen Song |
| Institution: | 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. |
| Keywords: | Banach space Generalized forward-backward splitting method Generalized proximity operator P-duality mapping |