This paper addresses the design of hybrid precoders in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, which combine digital and analog precoders to overcome the limitations of fully digital precoding in terms of cost and power consumption. The authors propose alternating minimization (AltMin) algorithms for two hybrid precoding structures: fully-connected and partially-connected. For the fully-connected structure, an AltMin algorithm based on manifold optimization is developed to approach the performance of the fully digital precoder, but it has high complexity. To address this, a low-complexity AltMin algorithm, PE-AltMin, is proposed by enforcing an orthogonal constraint on the digital precoder. For the partially-connected structure, an AltMin algorithm using semidefinite relaxation is developed. The proposed algorithms are extended to broadband OFDM systems, and simulation results demonstrate significant performance gains over existing hybrid precoding algorithms. The PE-AltMin algorithm is particularly useful for practical implementation due to its low complexity and effectiveness in achieving near-optimal performance.This paper addresses the design of hybrid precoders in millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems, which combine digital and analog precoders to overcome the limitations of fully digital precoding in terms of cost and power consumption. The authors propose alternating minimization (AltMin) algorithms for two hybrid precoding structures: fully-connected and partially-connected. For the fully-connected structure, an AltMin algorithm based on manifold optimization is developed to approach the performance of the fully digital precoder, but it has high complexity. To address this, a low-complexity AltMin algorithm, PE-AltMin, is proposed by enforcing an orthogonal constraint on the digital precoder. For the partially-connected structure, an AltMin algorithm using semidefinite relaxation is developed. The proposed algorithms are extended to broadband OFDM systems, and simulation results demonstrate significant performance gains over existing hybrid precoding algorithms. The PE-AltMin algorithm is particularly useful for practical implementation due to its low complexity and effectiveness in achieving near-optimal performance.