On the asymptotical regularization with convex constraints for nonlinear ill-posed problems

We investigate the method of asymptotical regularization for solving nonlinear illposed problems F(x) = y in Hilbert spaces. A general uniformly convex functional has been embedded in the evolution equations which is allowed to be non-smooth, thus the algorithm can be applied for sparsity and discontinuity reconstruction. Assuming certain conditions concerning the nonlinear operator F and functional Theta, we establish the convergence and stability of the method. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

We investigate the method of asymptotical regularization for solving nonlinear illposed problems F(x) = y in Hilbert spaces. A general uniformly convex functional has been embedded in the evolution equations which is allowed to be non-smooth, thus the algorithm can be applied for sparsity and discontinuity reconstruction. Assuming certain conditions concerning the nonlinear operator F and functional Theta, we establish the convergence and stability of the method.