Preprint D124/2015
Projective acceleration of the nonlinear Landweber method under the tangential cone condition
Antonio Leitao | Benar Svaiter

We use convex analysis to devise an iterative method for solving ill-posed problems modeled by nonlinear operators acting between Hilbert spaces. The tangential cone condition (TCC) is our starting point for defining special convex sets possessing a separation property. This is the key ingredient to define an iterative method based on successive orthogonal projections onto these sets. Since the stepsize of this new method happens to be a multiple of the Landweber (LW) iteration stepsize, we call this new method projective LW (PLW). Conversely, by introducing relaxation in the projection of the PLW method we obtain a family of methods that include LW and LW method with line-search (LWls). Moreover, the convergence analysis of this family provides a unified framework for all above mentioned methods under the TCC. Numerical experiments are presented for a nonlinear 2D elliptic parameter identification problem, validating the efficiency of the PLW method compared with the well known LW and LWls iterations.