Intelligent reflecting surfaces (IRSs) are regarded as key enablers of next-generation wireless communications, due to their capability of customizing the wireless propagation environment. In this paper, we investigate power-efficient resource allocation for IRS-assisted multiuser multiple-input single-output (MISO) systems. To minimize the transmit power, both the beamforming vectors at the access point (AP) and phase shifts at the IRS are jointly optimized while taking into account the minimum required quality-of-service (QoS) of the users. To tackle the non-convexity of the formulated optimization problem, an inner approximation (IA) algorithm is developed. Unlike existing designs, which cannot guarantee local optimality, the proposed algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) solution. Our simulation results show the effectiveness of the proposed algorithm compared to baseline schemes and reveal that deploying IRSs is more promising than leveraging multiple antennas at the AP in terms of energy efficiency.