Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems

The paper introduces the Anchored Extra-Proximal (AEP) framework for solving composite monotone inclusion problems, combining anchored extrapolation with an inexact anchored proximal update. By replacing the operator in the implicit update with its Taylor approximation and using a bisection line search, the authors derive a pth-order method that achieves a tangent-residual error ε in “~O(ε^{-2/(3p-1)})” oracle calls for every p ≥ 2. This complexity matches a proven lower bound, establishing the method as optimally efficient for deterministic algorithms in the pth-order oracle model.

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