This paper presents a non-perturbative solution to the inverse scattering problem with application to diffraction tomography. The proposed inverse problem formulation is based on non-linear optimization techniques, while the unknown internal field is expressed in a limited number of plane waves and the scatterer is expanded in terms of Gaussian basis functions. Different optimization methods are employed and compared in terms of their performance. In addition, an experimental diffraction tomography prototype scanner is built in order to further validate the proposed method.