In this letter, we consider the fundamental problem of jointly designing the transmit beamformers and the phase-shifts of the intelligent reflecting surface (IRS) / reconfigurable intelligent surface (RIS) to minimize the transmit power, subject to quality-of-service constraints at individual users in an IRS-assisted multiuser multiple-input single-output downlink communication system. In particular, we propose a new successive convex approximation based second-order cone programming approach in which all the optimization variables are simultaneously updated in each iteration. Our proposed scheme achieves superior performance compared to state-of-the-art benchmark solutions. In addition, the complexity of the proposed scheme is $O(N_{\mathrm s}^{3.5})$, while that of state-of-the-art benchmark schemes is $O(N_{\mathrm s}^{7})$, where $N_{\mathrm s}$ denotes the number of reflecting elements at the IRS.