  We propose and analyze a family of successive projection methods whose step
direction is the same as Landweber method for solving nonlinear 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 parameter
identification problem, validating the efficiency of our method.
