Whenever we wish to determine the characteristics of an object based on data of how it scatters incoming radiation we must solve an inverse scattering problem. This is a frequent situation in many fields, such as geophysical imaging or biomedical imaging. To reconstruct objects from the measured data, we can design optimization problems in which the boundary value problems governing the incident radiation act as constraints. Then we implement descent techniques to approach a global minimum. However, the process may stagnate without converging, either due to lack of convexity or to small gradients. We propose a method to overcome this difficulty combining topological derivative based optimization to generate first approximations with iteratively regularized Gauss-Newton techniques to ensure convergence. Numerical simulations illustrate fast reconstruction of objects formed by multiple non convex components in extreme situations such as holographic microscopy set-ups, in which the only data available are intensity measurements for one incident light beam on a limited screen.