Relaxed Gauss--Newton Methods with Applications to Electrical Impedance Tomography

As second-order methods, Gauss--Newton-type methods can be more effective\nthan first-order methods for the solution of nonsmooth optimization problems\nwith expensive-to-evaluate smooth components. Such methods, however, often do\nnot converge. Motivated by nonlinear inverse problems with nonsmooth\nregularization, we propose a new Gauss--Newton-type method with inexact relaxed\nsteps. We prove that the method converges to a set of disjoint critical points\ngiven that the linearisation of the forward operator for the inverse problem is\nsufficiently precise. We extensively evaluate the performance of the method on\nelectrical impedance tomography (EIT).\n