Nonlinear modified newton minimization of reduced-order objective functions for two-parameter inversion problems

We present a modified Newton minimization scheme for two-parameter inversion problems. Starting point is a so-called reduced-order objective function which measures the discrepancy between measured data and model-order reduction scattered field data. This objective function is minimized on a specified range of permittivity and conductivity values and a nonlinear transformation turns this constraint minimization problem into an unconstraint one. A backtracking procedure to obtain proper step lengths is implemented as well and a numerical example illustrates the performance of the method.