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This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signal-to-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the non-convex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unit-modulus constraints. {We also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration.} Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the state-of-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction.