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An accelerated inexact proximal point method for solving nonconvex-concave min-max problems

arXiv 1905.13433 ↗First posted 31 May 2019math.OCcited by 30

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Abstract (arXiv)

This paper presents smoothing schemes for obtaining approximate stationary points of unconstrained or linearly-constrained composite nonconvex-concave min-max (and hence nonsmooth) problems by applying well-known algorithms to composite smooth approximations of the original problems. More specifically, in the unconstrained (resp. constrained) case, approximate stationary points of the original problem are obtained by applying, to its composite smooth approximation, an accelerated inexact proximal point (resp. quadratic penalty) method presented in a previous paper by the authors. Iteration complexity bounds for both smoothing schemes are also established. Finally, numerical results are given to demonstrate the efficiency of the unconstrained smoothing scheme.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 May 2019.

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

30 papers.

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  1. 2021Independent Policy Gradient Methods for Competitive Reinforcement Learningcited by 97
  2. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 50
  3. 2023First-order penalty methods for bilevel optimizationcited by 40
  4. 2021Complexity Lower Bounds for Nonconvex-Strongly-Concave Min-Max Optimizationcited by 34
  5. 2022Stochastic Differentially Private and Fair Learningcited by 16
  6. 2024Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimizationcited by 15
  7. 2021Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problemscited by 10
  8. 2022First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spacescited by 10
  9. 2022Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problemscited by 10
  10. 2023Solving a Class of Non-Convex Minimax Optimization in Federated Learningcited by 10
  11. 2022On Convergence of Gradient Descent Ascent: A Tight Local Analysiscited by 9
  12. 2021Minimax Optimization with Smooth Algorithmic Adversariescited by 8
18 more
  1. 2021Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domaincited by 8
  2. 2023A first-order augmented Lagrangian method for constrained minimax optimizationcited by 8
  3. 2021Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problemscited by 7
  4. 2022Tight Analysis of Extra-gradient and Optimistic Gradient Methods For Nonconvex Minimax Problemscited by 7
  5. 2024Proximal Oracles for Optimization and Samplingcited by 5
  6. 2022STay-ON-the-Ridge: Guaranteed Convergence to Local Minimax Equilibrium in Nonconvex-Nonconcave Gamescited by 4
  7. 2023f-FERM: A Scalable Framework for Robust Fair Empirical Risk Minimizationcited by 4
  8. 2021Randomized Stochastic Gradient Descent Ascentcited by 3
  9. 2024A Fully Parameter-Free Second-Order Algorithm for Convex-Concave Minimax Problemscited by 3
  10. 2025Solving bilevel optimization via sequential minimax optimizationcited by 3
  11. 2024Two trust region type algorithms for solving nonconvex-strongly concave minimax problemscited by 2
  12. 2023An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problemscited by 1
  13. 2024Stochastic Compositional Minimax Optimization with Provable Convergence Guaranteescited by 1
  14. 2025Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulationcited by 1
  15. 2022Iterative Minimax Games with Coupled Linear Constraintscited by 0
  16. 2024Completely Parameter-Free Single-Loop Algorithms for Nonconvex-Concave Minimax Problemscited by 0
  17. 2024Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problemscited by 0
  18. 2025A first-order method for nonconvex-strongly-concave constrained minimax optimizationcited by 0