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

arXiv: https://arxiv.org/abs/1905.13433 · HTML: https://mlsanity.com/paper/1905.13433/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 30 of 30)

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- [Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problems](https://mlsanity.com/paper/2112.09579/) (2021)
- [First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spaces](https://mlsanity.com/paper/2206.02041/) (2022)
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- [Minimax Optimization with Smooth Algorithmic Adversaries](https://mlsanity.com/paper/2106.01488/) (2021)
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- [A first-order augmented Lagrangian method for constrained minimax optimization](https://mlsanity.com/paper/2301.02060/) (2023)
- [Derivative-free Alternating Projection Algorithms for General Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/2108.00473/) (2021)
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- [Proximal Oracles for Optimization and Sampling](https://mlsanity.com/paper/2404.02239/) (2024)
- [STay-ON-the-Ridge: Guaranteed Convergence to Local Minimax Equilibrium in Nonconvex-Nonconcave Games](https://mlsanity.com/paper/2210.09769/) (2022)
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- [A Fully Parameter-Free Second-Order Algorithm for Convex-Concave Minimax Problems](https://mlsanity.com/paper/2407.03571/) (2024)
- [Solving bilevel optimization via sequential minimax optimization](https://mlsanity.com/paper/2511.07398/) (2025)
- [Two trust region type algorithms for solving nonconvex-strongly concave minimax problems](https://mlsanity.com/paper/2402.09807/) (2024)
- [An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems](https://mlsanity.com/paper/2310.15448/) (2023)
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- [Enhancing Stability of Physics-Informed Neural Network Training Through Saddle-Point Reformulation](https://mlsanity.com/paper/2507.16008/) (2025)
- [Iterative Minimax Games with Coupled Linear Constraints](https://mlsanity.com/paper/2212.04672/) (2022)
- [Completely Parameter-Free Single-Loop Algorithms for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/2407.21372/) (2024)
- [Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problems](https://mlsanity.com/paper/2411.15769/) (2024)
- [A first-order method for nonconvex-strongly-concave constrained minimax optimization](https://mlsanity.com/paper/2512.22909/) (2025)

## 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.