Optimal (N-1)-step fixed-point algorithms correspond exactly to (N-1)! arc diagrams that support composition, decomposition, and H-duality while producing new quasi-anytime optimal methods.
From Halpern’s fixed-point iterations to Nesterov’s accelerated interpretations for root-finding problems.Computational Optimization and Applications, 87(1):181–218
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A Theory of Composition and Duality of Extremal Optimal Fixed-Point Algorithms
Optimal (N-1)-step fixed-point algorithms correspond exactly to (N-1)! arc diagrams that support composition, decomposition, and H-duality while producing new quasi-anytime optimal methods.