mlsanityData to 14 Oct 2026

Convergence of Proximal Point and Extragradient-Based Methods Beyond Monotonicity: the Case of Negative Comonotonicity

arXiv 2210.13831 ↗First posted 25 Oct 2022math.OCcited by 16

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Abstract (arXiv)

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim, 2021, Pethick et al., 2022, B"ohm, 2022] aiming at going beyond monotonicity by considering the weaker negative comonotonicity assumption. In particular, we provide tight complexity analyses for the Proximal Point, Extragradient, and Optimistic Gradient methods in this setup, closing some questions on their working guarantees beyond monotonicity.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 Oct 2022.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 3; 2023: 8; 2024: 2; 2025: 1; 2026: 2.

16 papers.

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  1. 2023Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditionscited by 14
  2. 2022Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimizationcited by 12
  3. 2022Beyond the Golden Ratio for Variational Inequality Algorithmscited by 12
  4. 2023Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalitiescited by 7
  5. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  6. 2025Expected Variational Inequalitiescited by 5
  7. 2026Solving Stochastic Variational Inequalities without the Bounded Variance Assumptioncited by 5
  8. 2023Two-timescale Extragradient for Finding Local Minimax Pointscited by 4
  9. 2023Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updatescited by 4
  10. 2024Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexitycited by 4
  11. 2023Stable Nonconvex-Nonconcave Training via Linear Interpolationcited by 3
  12. 2023Optimal Guarantees for Algorithmic Reproducibility and Gradient Complexity in Convex Optimizationcited by 3
4 more
  1. 2024Revisiting Extragradient-Type Methods -- Part 1: Generalizations and Sublinear Convergence Ratescited by 2
  2. 2022When is Momentum Extragradient Optimal? A Polynomial-Based Analysiscited by 1
  3. 2023Convergence of the Chambolle-Pock Algorithm in the Absence of Monotonicitycited by 1
  4. 2026Polyak-Type Extragradient Methods for Monotone Root-Finding Problemscited by 0