In this paper, we show that tracking multiple people whose paths may intersect can be formulated as a convex global optimization problem. Our proposed framework is designed to exploit image appearance cues to prevent identity switches. Our method is effective even when such cues are only available at distant time intervals. This is unlike many current approaches that depend on appearance being exploitable from frame to frame. We validate our approach on three multi-camera sport and pedestrian datasets that contain long and complex sequences. Our algorithm perseveres identities better than state-of-the-art algorithms while keeping similar MOTA scores.