Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.
Springer, 2017
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The MAEG-R method achieves convergence for monotone inclusions with merely continuous operators via a moving-anchor restart strategy, while preserving O(1/k) complexity in the Lipschitz case.
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Higher-Order Derivatives Do Not Accelerate the Computation of Fixed Points
Finite-order derivative information cannot accelerate worst-case fixed-point computation for smooth contractive mappings, proving Picard iteration is exactly optimal.
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Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity
The MAEG-R method achieves convergence for monotone inclusions with merely continuous operators via a moving-anchor restart strategy, while preserving O(1/k) complexity in the Lipschitz case.