This paper considers hybrid beamforming by combining an analog beamformer with a new regularized zero forcing baseband one, for multi-user millimeter-wave networks under a limited number of radio frequency (RF) chains. Three popular scenarios are examined: i) the number of users is up to the number of RF chains in a single-cell network, ii) the number of users is up to twice the number of RF chains in a singlecell network, and iii) the number of users is up to twice the number of RF chains in each cell of a two-cell network. In the second and third scenarios, we group the users into two categories of cell-center users as well as cell-edge users and serve them in two different time fractions. In the third scenario, we propose to suppress the inter-cell interference by serving the cell-center and cell-edge users in alternate fractional-time slots. In all the three scenarios, we determine the optimal power allocation maximizing the users’ minimum rate. Finally, lowcomplexity path-following algorithms having rapid convergence are developed for the computation of the optimal power. Our simulation results show that the proposed algorithms achieve a clear performance gain over the existing benchmarkers.