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Anchored Extra-Proximal Methods: Optimal Higher-Order Methods for Monotone Inclusion Problems
We study the deterministic oracle complexity of finding approximate solutions to composite monotone inclusion problems, formed by the sum of a smooth single-valued monotone operator and a maximally monotone set-valued operator, under the tangent-residual criterion. We introduce the Anchored Extra-Proximal (AEP) framework, which combines an anchored extrapolation step with an inexact anchored proximal update satisfying a relative-error condition. The framework recovers the composite Fast Extragradient method in the first-order setting and yields natural second- and higher-order extensions by re
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Evidence & attribution
- arXiv · AI, language, vision and robotics · 2026-09-24T17:43:45.000Z
First collected: 2026-09-25T06:12:46.948Z. This is not the publication date.