Millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems realizing directive beamforming require reliable estimation of the wireless propagation channel. However, mmWave channels are characterized by high variability that severely challenges their recovery over short training periods. Current channel estimation techniques exploit either the channel sparsity in the beamspace domain or its low-rank property in the antenna domain, nevertheless, they still require large numbers of training symbols for the satisfactory performance. In this letter, we present a novel channel estimation algorithm that jointly exploits the latter two properties of mmWave channels to provide more accurate recovery, especially for shorter training intervals. The proposed iterative algorithm is based on the alternating direction method of multipliers and provides the global optimum solution to the considered convex mmWave channel estimation problem with fast convergence properties.