A network relying on a large antenna-array-aided base station is designed for delivering multiple information streams to multi-antenna users over high-frequency bands such as the millimeter-wave and sub-Terahertz bands. The state-of-the-art analog precoder (AP) dissipates excessive circuit power due to its reliance on a large number of phase shifters. To mitigate the power consumption, we propose a novel AP relying on a controlled number of phase shifters. Within this new AP framework, we design a hybrid precoder (HP) for maximizing the users' minimum throughput, which poses a computationally challenging problem of large-scale, nonsmooth mixed discrete-continuous log-determinant optimization. To tackle this challenge, we develop an algorithm which iterates through solving convex problems to generate a sequence of HPs that converges to the max-min solution. We also introduce a new framework of smooth optimization termed soft max-min throughput optimization. Additionally, we develop another algorithm, which iterates by evaluating closed-form expressions to generate a sequence of HPs that converges to the soft max-min solution. Simulation results reveal that the HP soft max-min solution approaches the Pareto-optimal solution constructed for simultaneously optimizing both the minimum throughput and sum-throughput. Explicitly, it achieves a minimum throughput similar to directly maximizing the users' minimum throughput and it also attains a sum-throughput similar to directly maximizing the sum-throughput.