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Choice of the Parameters in A Primal-Dual Algorithm for Bregman Iterated Variational Regularization. (arXiv:1807.05793v1 [math.NA])
来源于:arXiv
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>>