Daniel Gerth, Stefan Kindermann
Published 2019-05-24Version 1
We show that a Kurdyka-\L{}ojasiewicz (KL) inequality can be used as regularity condition for Tikhonov regularization with linear operators in Banach spaces. In fact, we prove the equivalence of a KL inequality and various known regularity conditions (variational inequality, rate conditions, and others) that are utilized for postulating smoothness conditions to obtain convergence rates. Case examples of rate estimates for Tikhonov regularization with source conditions or with conditional stability estimate illustrate the theoretical result.
Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints
Regularization of Inverse Problems
A regularity condition under which integral operators with operator-valued kernels are trace class
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