The high training cost of the massive multiple-input multiple-output (MIMO) systems motivates the use of hybrid digital/analog (HDA) beamforming structures. This paper considers the joint design of analog beamformers when both link ends of a millimeter (mm)-wave massive MIMO system are equipped with such HDA structures. We aim to maximize the multi-user MIMO net average throughput of the downlink in a frequency division duplex system. To achieve this, we develop an optimization framework, namely, user-centric virtual sectorization (UCVS), to explore the tradeoff of training overhead, beamforming gain, and spatial multiplexing gain. In the UCVS, both the channel-statistics-based analog beamforming design and a non-orthogonal downlink training scheme are investigated to reduce the necessary cost of instantaneous channel acquisition. By maximizing an approximate net average throughput, we devise efficient algorithms to realize the suboptimal UCVS. With generic mm-wave channel models, we demonstrate by simulations that our proposed scheme outperforms the state-of-the-art methods in various typical scenarios of mm-wave communications.