In this work we analyze the inverse problem of recovering a space-dependent potential
coefficient in an elliptic/parabolic problem from distributed observation. We establish novel …

We shall study in this paper the convergence rates of the Tikhonov regularized solutions for
the recovery of the radiativities in elliptic and parabolic systems in general dimensional …

We investigate semismooth Newton and quasi-Newton methods for minimization problems
arising from weighted ℓ1-regularization. We give proofs of the local convergence of these …

We investigate the convergence rates for total variation regularization of the problem of
identifying (i) the coefficient q in the Neumann problem for the elliptic equation, and (ii) the …

In this chapter are outlined some aspects of the mathematical theory for direct regularization
methods aimed at the stable approximate solution of nonlinear illposed inverse problems …

Descent gradient methods are the most frequently used algorithms for computing
regularizers of inverse problems. They are either directly applied to the discrepancy term …

Selecting the best regularization parameter in inverse problems is a classical and yet
challenging problem. Recently, data-driven approaches based on supervised learning have …

We investigate the convergence rates for total variation regularization of the problem of
identifying (i) the coefficient q in the Neumann problem for the elliptic equation− div (q∇ u) …

In this paper, we analyze gradient methods for minimization problems arising in the
regularization of nonlinear inverse problems with sparsity constraints. In particular, we study …

This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator
equations in Banach spaces. As the main challenge, we consider the so-called …