The problem of reconstructing impedance distribution of the screen providing the desired distribution of the resulting field in the far zone is under discussion. Radiation patterns with a sharp drop (cut-off) at the transition to the shadow area is of special interest. The problem refers to the solution of the nonlinear inverse problem of electromagnetics. Weakly-directional radiation source field diffracted by a semi-transparent screen with a variable impedance profile is under consideration. The initial formulation of the problem is equivalent to the solution of the integral equation of the second kind. The procedure of impedance synthesis based on the numerical solution of the integral equation by the method of moments is constructed. The analytical solution of the problem is proposed for the first step of synthesis, and numerical optimization methods are applied to further synthesis process. To eliminate heavily oscillating solutions, the Tikhonov regularization method is applied. Heuristic algorithms for searching the global minimum are supplemented by quasi-Newtonian algorithms for further refinement of the solution at the last step. Numerical estimates of the values of realised radiation pattern cutoffs are discussed for different geometrical sizes of the screen.