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We introduce and analyze a fast iterative method based on sequential Bregmanprojections for nonlinear inverse problems in Banach spaces. The key idea, incontrast to the standard Landweber method, is to use multiple search directionsper iteration in combination with a regulation of the step width in order toreduce the total number of iterations. This method is suitable for both exactand noisy data. In the latter case, we obtain a regularization method. Analgorithm with two search directions is used for the numerical identificationof a parameter in an elliptic boundary value problem.

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