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Towards Tikhonov regularization of non-linear ill-posed problems: a dc programming approach. (English. Abridged French version) Zbl 1018.65072

Summary: 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.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47J06 Nonlinear ill-posed problems
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