We present a new method for determining the complex dielectric permittivity profile of 3-D inhomogeneous dielectric objects from measurements of the scattered electric field vectors in the frequency domain. The method is formulated as a minimization of a cost function defined in terms of electric field integral equations known as the object and data equations. Instead of an unknown object function containing the electromagnetic parameters of the dielectrics, the contrast sources induced within the scatterers are designated as the unknowns of the inversion scheme to avoid solving the forward scattering problem at each step. Later, the minimization of the cost function is achieved via a limited-memory quasi-Newton scheme, based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula, which iteratively updates the Hessian matrix estimation. The numerical results with the simulated and experimental scattered electric fields demonstrate that the presented method is capable of reconstructing scatterers with complex shapes.