mlsanityData to 7 Oct 2026

A first-order augmented Lagrangian method for constrained minimax optimization

arXiv 2301.02060 ↗First posted 5 Jan 2023math.OC cs.LG cs.NAcited by 8

Not on the map. Why?

Abstract (arXiv)

In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method developed in this paper. Under some suitable assumptions, an operation complexity of O(varepsilon-4logvarepsilon-1), measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an varepsilon-KKT solution of the constrained minimax problems.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 42 of its 79 references that are in the map. First posted on arXiv 5 Jan 2023.

Builds on

42 of 79 references.

References · 42

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  4. 2019On Gradient Descent Ascent for Nonconvex-Concave Minimax Problemscited by 266
  5. 2019DualDICE: Behavior-Agnostic Estimation of Discounted Stationary Distribution Correctionscited by 254
  6. 2013Optimization, Learning, and Games with Predictable Sequencescited by 187
  7. 2016Variance-based regularization with convex objectivescited by 153
  8. 2015Fast Convergence of Regularized Learning in Gamescited by 149
  9. 2019Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methodscited by 148
  10. 2018A Variational Inequality Perspective on Generative Adversarial Networkscited by 144
  11. 2020Perceptual Adversarial Robustness: Defense Against Unseen Threat Modelscited by 137
  12. 2015Distributionally Robust Logistic Regressioncited by 124
30 more
  1. 2020Near-Optimal Algorithms for Minimax Optimizationcited by 119
  2. 2018Multi-Agent Generative Adversarial Imitation Learningcited by 99
  3. 2019Efficient Algorithms for Smooth Minimax Optimizationcited by 75
  4. 2020Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problemscited by 75
  5. 2018Weakly-Convex Concave Min-Max Optimization: Provable Algorithms and Applications in Machine Learningcited by 62
  6. 2020A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problemscited by 57
  7. 2017Stochastic Variance Reduction Methods for Policy Evaluationcited by 56
  8. 2020A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problemscited by 56
  9. 2019Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applicationscited by 55
  10. 2018On the Convergence and Robustness of Training GANs with Regularized Optimal Transportcited by 51
  11. 2023First-order penalty methods for bilevel optimizationcited by 40
  12. 2020Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimizationcited by 39
  13. 2019Adversarial Attack Generation Empowered by Min-Max Optimizationcited by 32
  14. 2019An accelerated inexact proximal point method for solving nonconvex-concave min-max problemscited by 30
  15. 2020Adaptive extra-gradient methods for min-max optimization and gamescited by 30
  16. 2019An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraintscited by 29
  17. 2020Single-Timescale Stochastic Nonconvex-Concave Optimization for Smooth Nonlinear TD Learningcited by 24
  18. 2022The First Optimal Algorithm for Smooth and Strongly-Convex-Strongly-Concave Minimax Optimizationcited by 20
  19. 2020Fast Objective & Duality Gap Convergence for Non-Convex Strongly-Concave Min-Max Problems with PL Conditioncited by 19
  20. 2019Complexity of Proximal augmented Lagrangian for nonconvex optimization with nonlinear equality constraintscited by 17
  21. 2021Proximal Gradient Descent-Ascent: Variable Convergence under KL Geometrycited by 17
  22. 2020A Primal-Dual Smoothing Framework for Max-Structured Non-Convex Optimizationcited by 14
  23. 2022A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimizationcited by 12
  24. 2019On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimizationcited by 10
  25. 2021Convex-Concave Min-Max Stackelberg Gamescited by 9
  26. 2020Adversarial Classification via Distributional Robustness with Wasserstein Ambiguitycited by 8
  27. 2019Complexity and performance of an Augmented Lagrangian algorithmcited by 6
  28. 2020Optimality Conditions for Constrained Minimax Optimizationcited by 6
  29. 2021Minimax Problems with Coupled Linear Constraints: Computational Complexity, Duality and Solution Methodscited by 4
  30. 2022Optimality Conditions and Numerical Algorithms for A Class of Linearly Constrained Minimax Optimization Problemscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 4.

8 papers.

  1. 2023Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimizationcited by 6
  2. 2025Solving bilevel optimization via sequential minimax optimizationcited by 3
  3. 2026Achieving Better Local Regret Bound for Online Non-Convex Bilevel Optimizationcited by 1
  4. 2026Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problemscited by 1
  5. 2024Accelerated Fully First-Order Methods for Bilevel and Minimax Optimizationcited by 0
  6. 2025A first-order method for nonconvex-strongly-concave constrained minimax optimizationcited by 0
  7. 2026Fully First-Order Algorithms for Online Bilevel Optimizationcited by 0
  8. 2026Bilevel Optimization with Lower-Level Uniform Convexity: Theory and Algorithmcited by 0