Clipping is a necessary signal processing operation in many realtime audio applications, yet it often reduces the sound quality of the signal. The recently proposed perception-based clipping algorithm has been shown to significantly outperform other clipping techniques in terms of objective sound quality scores. However, the real-time solution of the optimization problems that form the core of this algorithm, poses a challenge. In this paper, a fast gradient projection optimization method is proposed and incorporated into the perceptionbased clipping algorithm. The optimization method will be shown to have an extremely low computational complexity per iteration, allowing the perception-based clipping algorithm to be applied in real-time for a broad range of clipping factors.