Recent Developments in Inverse Problems - Abstract

Hans, Esther

Globally convergent Bouligand-semismooth Newton methods for $ell_1$ Tikhonov regularization

We are concerned with Tikhonov regularization of (non)linear ill-posed problems with $ell_1$ coefficient penalties. We present a globalized Bouligand-semismooth Newton method for the efficient minimization of the corresponding Tikhonov functionals, where globalization is achieved by a damping strategy and suitable descent with respect to an associated merit functional. Due to their locally superlinear convergence, semismooth Newton methods are particularly competitive in comparison to existing iterative, globally convergent approaches. Furthermore, in the case of linear inverse problems, the Tikhonov minimizer is found within finitely many iterations. medskip The results are based on joint work with Thorsten Raasch. beginthebibliography bibitemHaRa15 sc E. Hans and T. Raasch, em Global convergence of damped semismooth Newton methods for $ell_1$ Tikhonov regularization, Inverse Problems, 31 (2015), 025005. endthebibliography