A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification

We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per iteration in combination with a regulation of the step width in order to reduce the total number of iterations. This method is suitable for both exact and noisy data. In the latter case, we obtain a regularization method. An algorithm with two search directions is used for the numerical identification of a parameter in an elliptic boundary value problem.