On the Regularizing Levenberg-marquardt Scheme in Banach Spaces

By making use of duality mappings and the Bregman distance, we propose a regularizing Levenberg-Marquardt scheme to solve nonlinear inverse problems in Banach spaces, which is an extension of the one proposed in [6] in Hilbert space setting. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme involves a family of convex minimization problems in Banach spaces from which a suitable criterion is used to select one to produce the increments. The outer iteration is then terminated by a discrepancy principle. Under certain conditions, we establish the convergence of the method.