<p>The recently proposed restarted randomized surrounding algorithm improves the performance of the original randomized surrounding method by incorporating a restarting strategy. In this work, we introduce a fast restarted randomized surrounding algorithm that further accelerates convergence by integrating Polyak momentum. Compared to its predecessor, the proposed algorithm reduces the number of required iterations while maintaining nearly the same computational cost per iteration. We provide a rigorous convergence analysis to characterize the convergence rate of the proposed method. Numerical experiments demonstrate that the new algorithm outperforms existing reflection-based methods in both iteration count and total runtime.</p>