An iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented. The algorithm consists in solving a sequence of weighted l(1) convex optimization problems. The method can thus be readily implemented and efficiently solved. In the optimization procedure, the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements. The method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns. Numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach, whose computation time is several orders of magnitude below those of so-called global optimization algorithms.