Preprint D142/2018
On a family of gradient type projection methods for nonlinear ill-posed problems
Antonio Leitao | Benar Svaiter

We propose and analyze a family of successive projection methods
whose step direction is the same as Landweber method for solving non-
linear ill-posed problems that satisfy the Tangential Cone Condition
(TCC). This family enconpasses Landweber method, the minimal error
method, and the steepest descent method; thush providing an unified
framework for the analysis of these methods. Moreover, we define in
this family new methods which are convergent for the constant of the
TCC in a range twice as large as the one required for the Landweber
and other gradient type methods.
The TCC is widely used in the analysis of iterative methods for
solving nonlinear ill-posed problems. The key idea in this work is to
use the TCC in order to construct special convex sets possessing a
separation property, and to succesively project onto these sets.
Numerical experiments are presented for a nonlinear 2D elliptic pa-
rameter identification problem, validating the efficiency of our method.