The 2D inverse electromagnetic scattering problem of reconstructing the mat
erial properties of inhomogeneous lossy dielectric cylindrical objects is c
onsidered. The material properties are reconstructed using scattering data
from time-harmonic TM-polarized electromagnetic plane waves. A novel method
which ensures physically meaningful material properties is proposed to num
erically solve this non linear optimization problem. Numerical examples ill
ustrate the efficiency of the algorithm.