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A method for reconstructing the material properties of inhomogeneous lossy dielectric cylindrical objects is presented. The material properties are reconstructed using scattering data from time-harmonic electromagnetic plane waves with the electric field vector perpendicular to the cylindrical object (TE-polarization). The inverse scattering problem formulated as a nonlinear optimization problem is numerically solved using a variable metric method. This method involves exact first-order gradients. Numerical examples illustrate the efficiency of the algorithm.