Approximately regularized minimizer of the least squares functional with a non-smooth, convex penalty term and an indicator function is considered to be produced iteratively by some nested primal-dual algorithm. The algorithm is a proximal-gradient linesearch based iterative procedure and is introduced as an iterative variational regularization method. Under the consideration of that the exact solution for the linear ill-posed inverse problem satisfies a variational source condition (VSC), convergence of the regularized solution of the minimization problem to the exact solution, and convergence of the iteratively regularized approximate minimizer by our primal-dual algorithm to the exact solution are analysed separately. It is in the emphasis of this work that the regularization parameter obeys {\em Morozov`s discrepancy principle} (MDP) in order for the stability analysis of regularized solution. Furthermore, stability analysis of the algorithm requires us to define the additional par 查看全文>>