This paper is devoted to the problem of designing an H-2/H-infinity row-sparse static output feedback controller for continuous linear time-invariant systems with polytopic uncertainty. The immediate application of the proposed approach lies within the problem of the optimal selection of a subset of available actuators during the fault accommodation stage of a fault-tolerant control scheme. Incorporating an extra term for penalising the number of actuators into the optimisation objective function, we propose an explicit scheme and two iterative procedures according to the reweighted l(1) (REL1) and reweighted iterative support detection (RISD) algorithms for the purposes of identifying the favourable row-sparse feedback gains. Furthermore, this problem formulation allows us to incorporate additional constraints into the designing problem such as regional pole placement constraints which provide more control over the satisfactory transient behaviour and closed-loop pole locations. In this paper, we present two examples which demonstrate the remarkable performance and broad applicability of the proposed approaches.