  In this article we propose a novel strategy for choosing the Lagrange
multipliers in the Levenberg-Marquardt method for solving ill-posed problems
modeled by nonlinear operators acting between Hilbert spaces. Convergence
analysis results are established for the proposed method, including:
monotonicity of iteration error, geometrical decay of the residual, convergence
for exact data, stability and semi-convergence for noisy data. Numerical
experiments are presented for an elliptic parameter identification
two-dimensional EIT problem. The performance of our strategy is compared with
standard implementations of the Levenberg-Marquardt method (using a priori
choice of the multipliers).
