Abstract
Abstract
We consider the method of quasi-solutions (also referred to as Ivanov regularization) for the regularization of linear ill-posed problems in non-reflexive Banach spaces. Using the equivalence to a metric projection onto the image of the forward operator, it is possible to show regularization properties and to characterize parameter choice rules that lead to a convergent regularization method, which includes the Morozov discrepancy principle. Convergence rates in a suitably chosen Bregman distance can be obtained as well.
We also address the numerical computation of quasi-solutions to inverse source problems for partial differential equations in
{L^{\infty}(\Omega)}
using a semi-smooth Newton method and a backtracking line search for the parameter choice according to the discrepancy principle.
Numerical examples illustrate the behavior of quasi-solutions in this setting.
Funder
Deutsche Forschungsgemeinschaft
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