  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.
