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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N_{\mathrm {s}}^{3.5})$ </tex-math></inline-formula> , while that of state-of-the-art benchmark schemes is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N_{\mathrm {s}}^{7})$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{\mathrm {s}}$ </tex-math></inline-formula> denotes the number of reflecting elements at the IRS.
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