Operator Splitting Performance Estimation: Tight contraction factors and optimal parameter selection
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Abstract (arXiv)
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the methodology as a tool for computer-assisted proofs to prove tight analytical contraction factors for Douglas--Rachford splitting that are likely too complicated for a human to find bare-handed. Second, we use the methodology as an algorithmic tool to computationally select the optimal splitting method parameters by solving a series of semidefinite programs.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Dec 2018.
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Citing papers per year: 2021: 2; 2022: 2; 2023: 4; 2024: 2; 2025: 1; 2026: 2.
13 papers.
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- 2021Extragradient Method: O(1/K) Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivitycited by 39
- 2023Learning to Warm-Start Fixed-Point Optimization Algorithmscited by 32
- 2023Provably Faster Gradient Descent via Long Stepscited by 20
- 2022Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalitiescited by 18
- 2023Towards Constituting Mathematical Structures for Learning to Optimizecited by 13
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Pythoncited by 10
- 2025Negative Stepsizes Make Gradient-Descent-Ascent Convergecited by 9
- 2023From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learningcited by 5
- 2024Data-Driven Performance Guarantees for Classical and Learned Optimizerscited by 5
- 2024Enhancing Privacy in Federated Learning through Local Trainingcited by 3
- 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
- 2026RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolationcited by 0
1 more
- 2026Negative Momentum for Convex-Concave Optimizationcited by 0
- 2026Negative Momentum for Convex-Concave Optimization18 Apr 2026
- 2026RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation23 Mar 2026
- 2025Negative Stepsizes Make Gradient-Descent-Ascent Converge2 May 2025
- 2024Data-Driven Performance Guarantees for Classical and Learned Optimizers22 Apr 2024
- 2024Enhancing Privacy in Federated Learning through Local Training26 Mar 2024
- 2023Learning to Warm-Start Fixed-Point Optimization Algorithms14 Sep 2023
- 2023Provably Faster Gradient Descent via Long Steps12 Jul 2023
- 2023Towards Constituting Mathematical Structures for Learning to Optimize29 May 2023
- 2023From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning24 Feb 2023
- 2022Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities20 Apr 2022
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python11 Jan 2022
- 2021Extragradient Method: O(1/K) Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity8 Oct 2021
1 more
- 2021Extragradient Method: O(1/K) Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivitycited by 39
- 2023Learning to Warm-Start Fixed-Point Optimization Algorithmscited by 32
- 2023Provably Faster Gradient Descent via Long Stepscited by 20
- 2022Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalitiescited by 18
- 2023Towards Constituting Mathematical Structures for Learning to Optimizecited by 13
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Pythoncited by 10
- 2025Negative Stepsizes Make Gradient-Descent-Ascent Convergecited by 9
- 2023From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learningcited by 5
- 2024Data-Driven Performance Guarantees for Classical and Learned Optimizerscited by 5
- 2024Enhancing Privacy in Federated Learning through Local Trainingcited by 3
- 2021OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regressioncited by 1
- 2026RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolationcited by 0
12 most cited of 13 All 13 (JSON)
- 2026Negative Momentum for Convex-Concave Optimization18 Apr 2026
- 2026RAMPAGE: RAndomized Mid-Point for debiAsed Gradient Extrapolation23 Mar 2026
- 2025Negative Stepsizes Make Gradient-Descent-Ascent Converge2 May 2025
- 2024Data-Driven Performance Guarantees for Classical and Learned Optimizers22 Apr 2024
- 2024Enhancing Privacy in Federated Learning through Local Training26 Mar 2024
- 2023Learning to Warm-Start Fixed-Point Optimization Algorithms14 Sep 2023
- 2023Provably Faster Gradient Descent via Long Steps12 Jul 2023
- 2023Towards Constituting Mathematical Structures for Learning to Optimize29 May 2023
- 2023From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning24 Feb 2023
- 2022Tight Last-Iterate Convergence of the Extragradient and the Optimistic Gradient Descent-Ascent Algorithm for Constrained Monotone Variational Inequalities20 Apr 2022
- 2022PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python11 Jan 2022
- 2021Extragradient Method: O(1/K) Last-Iterate Convergence for Monotone Variational Inequalities and Connections With Cocoercivity8 Oct 2021
12 newest of 13 All 13 (JSON)