Inverse problems are inherently ill-posed, leading standard optimization techniques to fail and necessitating the use of regularization. This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. Our approach integrates regularization and structure exploitation directly within the Quasi-Newton framework, leveraging the strengths of Quasi-Newton methods, Tikhonov-type regularization, and structure exploitation. We provide a convergence analysis demonstrating local super-linear and weakly super-linear convergence in both infinite and finite dimensional settings. Furthermore, we discuss a globalization approach based on the dynamic control of the regularization parameter, which not only ensures global convergence but also provides an a priori method for the specific choice of the regularization parameter. The iterative adaptation of the regularization parameter within this globalization framework assures convergence even when starting far from the true solution of both the proposed method and the Levenberg-Marquardt method. By introducing compact representations of the proposed methods, we also enable efficient computation of Hessian approximations. These representations, particularly in limited-memory forms, are well-suited for large-scale inverse problems. Finally, we discuss a numerical example based on a PDE-driven parameter identification problem, relevant to industrial applications.
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