We propose a novel user equipment (UE) scheduling framework for millimeter-wave (mmWave) massive multiuser (MU) multiple-input multiple-output (MIMO) wireless systems. Our framework determines (sub)sets of UEs that should transmit simultaneously in a given time slot by approximately solving a nonconvex optimization problem using forward-backward splitting. Our UE scheduling framework is flexible in the sense that it (i) supports a variety of cost functions, including post-equalization mean square error and sum rate, and (ii) enables precise control over the minimum and maximum number of resources the UEs should occupy. We demonstrate the efficacy of our framework using realistic mmWave channel vectors generated with a commercial ray-tracer. We show that our UE scheduler outperforms a range of existing scheduling methods and closely approaches the performance of an exhaustive search.