mlsanityData to 7 Oct 2026

Golden Ratio Algorithms for Variational Inequalities

arXiv 1803.08832 ↗First posted 23 Mar 2018math.OC cs.NA math.NAcited by 38

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Abstract (arXiv)

The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a linesearch. Thus, each iteration of the method requires only one evaluation of a monotone operator F and a proximal mapping g. The operator F need not be Lipschitz-continuous, which also makes the algorithm interesting in the area of composite minimization where one cannot use the descent lemma. The method exhibits an ergodic O(1/k) convergence rate and R-linear rate, if F, g satisfy the error bound condition. We discuss possible applications of the method to fixed point problems. We discuss possible applications of the method to fixed point problems as well as its different generalizations.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Mar 2018.

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Citing papers per year: 2021: 6; 2022: 7; 2023: 11; 2024: 3; 2025: 4; 2026: 7.

38 papers.

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  1. 2021Faster Single-loop Algorithms for Minimax Optimization without Strong Concavitycited by 47
  2. 2021The Complexity of Nonconvex-Strongly-Concave Minimax Optimizationcited by 44
  3. 2022Accelerated Single-Call Methods for Constrained Min-Max Optimizationcited by 31
  4. 2023Adaptive Proximal Gradient Method for Convex Optimizationcited by 21
  5. 2021Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusionscited by 20
  6. 2021No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimizationcited by 20
  7. 2022Accelerated Algorithms for Constrained Nonconvex-Nonconcave Min-Max Optimization and Comonotone Inclusioncited by 19
  8. 2023Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradientcited by 19
  9. 2023A simple uniformly optimal method without line search for convex optimizationcited by 18
  10. 2022Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimizationcited by 16
  11. 2022Beyond the Golden Ratio for Variational Inequality Algorithmscited by 12
  12. 2023Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusionscited by 10
26 more
  1. 2022Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithmcited by 9
  2. 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
  3. 2024Adaptive and Optimal Second-order Optimistic Methods for Minimax Optimizationcited by 8
  4. 2021A first-order primal-dual method with adaptivity to local smoothnesscited by 7
  5. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  6. 2025Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimizationcited by 4
  7. 2021Cyclic Coordinate Dual Averaging with Extrapolationcited by 3
  8. 2024Primal Methods for Variational Inequality Problems with Functional Constraintscited by 3
  9. 2023Distributed Extra-gradient with Optimal Complexity and Communication Guaranteescited by 2
  10. 2023On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithmscited by 2
  11. 2024Auto-conditioned primal-dual hybrid gradient method and alternating direction method of multiplierscited by 2
  12. 2026Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusionscited by 2
  13. 2022Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustnesscited by 1
  14. 2022Primal-dual extrapolation methods for monotone inclusions under local Lipschitz continuitycited by 1
  15. 2025Layer-wise Quantization for Quantized Optimistic Dual Averagingcited by 1
  16. 2026Stochastic variance reduced extragradient methods for solving hierarchical variational inequalitiescited by 1
  17. 2026Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalitiescited by 1
  18. 2023Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionscited by 0
  19. 2023First-order methods for Stochastic Variational Inequality problems with Function Constraintscited by 0
  20. 2023An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problemscited by 0
  21. 2025A regret minimization approach to fixed-point iterationscited by 0
  22. 2025Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approachcited by 0
  23. 2026Breaking the Stochasticity Barrier: An Adaptive Variance-Reduced Method for Variational Inequalitiescited by 0
  24. 2026Adaptive Delayed-Update Cyclic Algorithm for Variational Inequalitiescited by 0
  25. 2026On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalitiescited by 0
  26. 2026Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Ratescited by 0