Infinitesimal dipole modeling (IDM) can model antennas analytically with small amounts of data. Constrained IDM has been proposed to improve the modeling efficiency by fixing the positions and orientations of the dipole elements. The restrictions have a tradeoff of the modeling requiring more dipole elements. Therefore, the modeling technique has the disadvantage of having low practicality. A recursive convex optimization based on reweighted l(1)-norm is proposed for sparse IDM. By applying the reweighted l(1)-norm to the convex optimization, the IDM can represent sparse solutions. Antennas can be modeled with dipole elements less than half of the previous constrained IDM. For verification, a five-patch array antenna and a slot array antenna are modeled by the proposed IDM scheme. About 57% and 45% of the dipole elements can be respectively suppressed using the proposed algorithm, with only 1 dB degradation in modeling accuracy.