Abstract

The Tikhonov regularization method for non-linear ill-posed problems requires us to globally solve non-convex optimization problem which have been very little studied in the inverse problems community. In this paper we suggest a method which is applicable to the Tikhonov method for a wide class of non-linear ill-posed problems. This is a class of problems when the Tikhonov functional for them can be represented by the difference of two convex functionals. Our method for these problems is a combination of the recently developed algorithm DCA in dc programming with the branch-and-bound techniques.