Transmit antenna selection (TAS) at base station has been widely studied and employed in many communication networks (such as those using massive multiple-input multiple-output (MIMO) systems). Thanks to the small size of microstrip antenna elements applicable to millimeter-wave (mmWave) frequencies, the implementation of TAS in small user equipments (UEs) employing switchable directional antennas is recently becoming popular. In this paper, we consider device-to-device (D2D) communications underlaying a cellular network wherein each D2D UE is equipped with switchable transmit antennas. By employing Generalized Bender’s Decomposition (GBD) algorithm, we obtained the solution to the problem of globally optimal transmit antenna selection and channel allocation to D2D UEs together with transmit powers of cellular and D2D UEs. Although we reformulated the non-convex primal subproblem of the proposed GBD-based method into convex form, we further managed to obtain the corresponding closed-form solution through analytical manipulations; this extensively increased (at least 60 times) the execution speed of the proposed method as shown in the simulation results.