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This paper introduces the use of adaptive restart to accelerate iterative hard thresholding (IHT) for low-rank matrix completion. First, we analyze the local convergence of accelerated IHT in the non-convex setting of matrix completion problem (MCP). We prove the linear convergence rate of the accelerated algorithm inside the region near the solution. Our analysis poses a major challenge to parameter selection for accelerated IHT when no prior knowledge of the "local Hessian condition number" is given.

We present a momentum-based accelerated iterative hard thresholding (IHT) for low-rank matrix completion. We analyze the convergence of the proposed Heavy Ball (HB) accelerated IHT near the solution and provide optimal step size parameters that guarantee the fastest rate of convergence. Since the optimal step sizes depend on the unknown structure of the solution matrix, we further propose a heuristic for parameter selection that is inspired by recent results in random matrix theory.