mlsanityData to 7 Oct 2026

Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions

arXiv 2201.12247 ↗First posted 28 Jan 2022math.OCcited by 27

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Abstract (arXiv)

We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called weak Minty solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of monotonicity. We prove novel convergence results for a generalized version of the optimistic gradient method (OGDA) in this setting, matching the 1/k rate for the best iterate in terms of the squared operator norm recently shown for the extragradient method (EG). In addition we propose an adaptive step size version of EG, which does not require knowledge of the problem parameters.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jan 2022.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 9; 2024: 2; 2025: 5; 2026: 5.

27 papers.

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  1. 2022Accelerated Single-Call Methods for Constrained Min-Max Optimizationcited by 31
  2. 2023Solving stochastic weak Minty variational inequalities without increasing batch sizecited by 21
  3. 2022Accelerated Algorithms for Constrained Nonconvex-Nonconcave Min-Max Optimization and Comonotone Inclusioncited by 19
  4. 2023Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradientcited by 19
  5. 2023Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditionscited by 14
  6. 2022Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noisecited by 13
  7. 2022Beyond the Golden Ratio for Variational Inequality Algorithmscited by 12
  8. 2022Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimizationcited by 11
  9. 2023Randomized Block-Coordinate Optimistic Gradient Algorithms for Root-Finding Problemscited by 9
  10. 2025Worst-case generation via minimax optimization in Wasserstein spacecited by 7
  11. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  12. 2025Expected Variational Inequalitiescited by 5
15 more
  1. 2023Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updatescited by 4
  2. 2024Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexitycited by 4
  3. 2025Extragradient Method for (L0, L1)-Lipschitz Root-finding Problemscited by 3
  4. 2024Diffusion Stochastic Optimization for Min-Max Problemscited by 2
  5. 2026Unbiased and Biased Variance-Reduced Forward-Reflected-Backward Splitting Methods for Stochastic Composite Inclusionscited by 2
  6. 2023An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problemscited by 1
  7. 2023Convergence of the Chambolle-Pock Algorithm in the Absence of Monotonicitycited by 1
  8. 2025A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Lojasiewicz conditioncited by 1
  9. 2026Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalitiescited by 1
  10. 2026How to Make the Gradient Mapping Small for Constrained Stochastic Min-Max Problems and Beyondcited by 1
  11. 2022Iterative Minimax Games with Coupled Linear Constraintscited by 0
  12. 2023Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionscited by 0
  13. 2025A first-order method for constrained nonconvex-nonconcave minimax optimizationcited by 0
  14. 2026Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusionscited by 0
  15. 2026On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalitiescited by 0