The 3GPP Release-13 has recently introduced full-dimension multiple-input multiple-output (FD-MIMO) technology as a practical way to deploy massive MIMO arrays within feasible base station (BS) form factors through the use of active antenna systems with two-dimensional (2D) planar array structures. The 2D arrangement of antenna elements, where the elements in each antenna port are fed with downtilt weights, allows for adaptive electronic beamforming in the elevation as well as the conventional azimuth dimensions. This work focuses on the previously unaddressed problem of determining the optimal downtilt weight vectors for the antenna ports in each cell of a multi-cell multi-user system. The optimization criterion is to maximize the minimum signal to intra-cell interference ratio within a cell while constraining the inter-cell interference leakage. The quasi-optimal weight vectors are obtained through the application of semi-definite relaxation and Dinkelbach's method. The proposed algorithm performs better than the existing approximate schemes even under the effects of pilot contamination.