mlsanityData to 14 Oct 2026

On the Convergence Properties of Non-Euclidean Extragradient Methods for Variational Inequalities with Generalized Monotone Operators

arXiv 1311.2776 ↗First posted 12 Nov 2013math.OCcited by 29

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Abstract (arXiv)

In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing approximate strong solutions of these problems, and demonstrate how their iteration complexities depend on the global Lipschitz or H"older continuity properties for their operators and the smoothness properties for the distance generating function used in the N-EG algorithms. We also introduce a variant of this algorithm by incorporating a simple line-search procedure to deal with problems with more general continuous operators. Numerical studies are conducted to illustrate the significant advantages of the developed algorithms over the existing ones for solving large-scale GMVI problems.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Nov 2013.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 6; 2024: 3; 2025: 1; 2026: 5.

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  1. 2021Policy Mirror Descent for Reinforcement Learning: Linear Convergence, New Sampling Complexity, and Generalized Problem Classescited by 156
  2. 2022Stochastic first-order methods for average-reward Markov decision processescited by 32
  3. 2022Accelerated Single-Call Methods for Constrained Min-Max Optimizationcited by 32
  4. 2021Decentralized Local Stochastic Extra-Gradient for Variational Inequalitiescited by 25
  5. 2022Accelerated Algorithms for Constrained Nonconvex-Nonconcave Min-Max Optimization and Comonotone Inclusioncited by 20
  6. 2021Distributed Methods with Compressed Communication for Solving Variational Inequalities, with Theoretical Guaranteescited by 15
  7. 2023On the Convergence of No-Regret Learning Dynamics in Time-Varying Gamescited by 14
  8. 2023Single-Call Stochastic Extragradient Methods for Structured Non-monotone Variational Inequalities: Improved Analysis under Weaker Conditionscited by 14
  9. 2022Universal Gradient Descent Ascent Method for Nonconvex-Nonconcave Minimax Optimizationcited by 12
  10. 2024Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyondcited by 11
  11. 2021Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problemscited by 10
  12. 2021A Decentralized Adaptive Momentum Method for Solving a Class of Min-Max Optimization Problemscited by 9
17 more
  1. 2021On the One-sided Convergence of Adam-type Algorithms in Non-convex Non-concave Min-max Optimizationcited by 9
  2. 2021Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domaincited by 8
  3. 2022Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problemscited by 7
  4. 2023Similarity, Compression and Local Steps: Three Pillars of Efficient Communications for Distributed Variational Inequalitiescited by 7
  5. 2022Perseus: A Simple and Optimal High-Order Method for Variational Inequalitiescited by 5
  6. 2023Sublinear Convergence Rates of Extragradient-Type Methods: A Survey on Classical and Recent Developmentscited by 5
  7. 2025Min-Max Optimisation for Nonconvex-Nonconcave Functions Using a Random Zeroth-Order Extragradient Algorithmcited by 5
  8. 2024Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexitycited by 4
  9. 2024Primal Methods for Variational Inequality Problems with Functional Constraintscited by 3
  10. 2026Multiscale replay: A robust algorithm for stochastic variational inequalities with a Markovian buffercited by 2
  11. 2022Semi-Implicit Hybrid Gradient Methods with Application to Adversarial Robustnesscited by 1
  12. 2026Non-KKT Accumulation in Entropic Mirror Descentcited by 1
  13. 2023Extragradient-Type Methods with O (1/k) Last-Iterate Convergence Rates for Co-Hypomonotone Inclusionscited by 0
  14. 2023First-order methods for Stochastic Variational Inequality problems with Function Constraintscited by 0
  15. 2026Non-Convex Sparse Reinforcement Learning via Non-Monotone Inclusionscited by 0
  16. 2026Establishing Boundary KKT Convergence of Mirror Descent through Reparameterizationcited by 0
  17. 2026Polyak-Type Extragradient Methods for Monotone Root-Finding Problemscited by 0