mlsanityData to 7 Oct 2026

Exact Optimal Accelerated Complexity for Fixed-Point Iterations

arXiv 2201.11413 ↗First posted 27 Jan 2022math.OCcited by 23

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Abstract (arXiv)

Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration mechanism for fixed-point iterations with nonexpansive operators, contractive operators, and nonexpansive operators satisfying a H"older-type growth condition. We then provide matching complexity lower bounds to establish the exact optimality of the acceleration mechanisms in the nonexpansive and contractive setups. Finally, we provide experiments with CT imaging, optimal transport, and decentralized optimization to demonstrate the practical effectiveness of the acceleration mechanism.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jan 2022.

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Citing papers per year: 2022: 1; 2023: 4; 2024: 5; 2025: 5; 2026: 8.

23 papers.

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  1. 2024PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compressioncited by 59
  2. 2022Accelerated Algorithms for Constrained Nonconvex-Nonconcave Min-Max Optimization and Comonotone Inclusioncited by 19
  3. 2025Towards Weaker Variance Assumptions for Stochastic Optimizationcited by 13
  4. 2024Stochastic Halpern iteration in normed spaces and applications to reinforcement learningcited by 11
  5. 2023Accelerating Value Iteration with Anchoringcited by 10
  6. 2023Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusionscited by 10
  7. 2024Fundamental Benefit of Alternating Updates in Minimax Optimizationcited by 9
  8. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  9. 2026Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularizationcited by 3
  10. 2024Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problemscited by 2
  11. 2025Model-Free Robust Average-Reward Reinforcement Learning with Sample Complexity Analysiscited by 2
  12. 2025Faster Fixed-Point Methods for Multichain MDPscited by 2
11 more
  1. 2025Finite-Time Bounds for Average-Reward Fitted Q-Iterationcited by 1
  2. 2025A Class of Accelerated Fixed-Point-Based Methods with Delayed Inexact Oracles and Its Applicationscited by 1
  3. 2026Learning Policy from a Single Trajectory in Average-Reward Markov Decision Processcited by 1
  4. 2023Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionscited by 0
  5. 2024HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restorationcited by 0
  6. 2026RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolationcited by 0
  7. 2026A Unifying View of Anchoring via Operator-Side Tikhonov Regularizationcited by 0
  8. 2026Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Ratescited by 0
  9. 2026Oracle Complexity of Stochastic Fixed-Point Equations with Nonexpansive Mapscited by 0
  10. 2026Stochastic Inertial Krasnosel'skii-Mann Iteration Achieves Near-Optimal Sample Complexitycited by 0
  11. 2026Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Findingcited by 0