Exact Optimal Accelerated Complexity for Fixed-Point Iterations
This paper introduces an accelerated method and a matching complexity lower bound for fixed-point iterations, proving its optimality under specific conditions like nonexpansive and contractive operators. The acceleration also extends to some settings where the operator exhibits Hölder-type growth. Practical experiments demonstrate some effectiveness, though further research is needed to assess the real-world impact across different problem domains and suboptimality measures.