We propose a new optimization scheme for solving electromagnetic inverse scattering problems. As known, they mean to retrieve the physical properties of hidden targets, i.e., the permittivity and/or permeability, from the measured scattering data excited by several incidences. By considering only the physical properties of the targets as unknowns, one usually resorts to the more traditional optimization searching scheme to find the solution, by which one needs to solve the corresponding forward problems for all the incidences at each iteration of the optimization, such as the well-known distorted Born iterative method (DBIM). This is often time-consuming even given the fast forward solvers. Later, a different optimization scheme, the modified gradient method, was proposed, where not only the physical properties of the targets are considered as unknowns but also the electric fields, which are simultaneously updated at each iteration of the optimization. From such a pioneering work, the same authors proposed the well-known contrast source inversion (CSI), considering the unknown to be the induced contrast sources instead of fields in order to form a new type of formulation. Compared to the original modified gradient method, the CSI method uses alternative optimization scheme so as to reduce the complexity of the nonlinear calculations. Considering the electric fields or the induced current as unknowns together with the permittivity/permeability, the inversion solver does not need to repetitively solve the forward problems as in the traditional inversion solvers mentioned above. In this talk, we further stretch the idea in the CSI to consider only the contrast sources as the unknowns by introducing a new type of formulations. While also avoiding to solve the forward problems at each iteration, the merits of doing so is to obtain different optimization paths in every inversion, each of which is di®erent from the one by the CSI method. Having such a new optimization scheme, one is able to justify the obtained reconstructed results by comparing them to each other and to the one obtained by the original CSI.