This paper considers a maximum-ratio transmitter (MRT) based-downlink transmission in a multi-user massive-MIMO system under the small-scale fading. The base-station is cost-constrained and can therefore afford only a limited number of RF chains. Likewise, the users have strict quality of service constraints (QoS) and therefore not all users can be served within the specified power budget. Specifically, such problems are combinatorial in nature and so an optimal solution can be obtained by running an exhaustive search over all possible set of antenna and user pairs that meet the QoS and simultaneously achieves the best rate. However, implementing the exhaustive search method is not viable for all practical applications due to the large size and consequently the intractable computational costs involved. Thus, a low complexity based joint antenna and user selection problem is formulated and solved using convex relaxation. Different from the existing techniques that rely on greedy approaches, the proposed algorithm yields near-optimal sum-rates and can be readily applied to very large systems. Detailed simulation results are presented to corroborate the near-optimality of the proposed scheme.