Nicolas Loizou, Hugo Berard, Alexia Jolicoeur-Martineau, Pascal Vincent, Simon Lacoste-Julien, and Ioannis Mitliagkas. Stochastic hamiltonian gradient methods for smooth games. In International Conference on Machine Learning, pages 6370-6381. PMLR, 2020.
Luo Luo, Yujun Li, and Cheng Chen. Finding second-order stationary points in nonconvex-strongly-concave minimax optimization. Advances in Neural Information Processing Systems, 35:36667-36679, 2022.
Panayotis Mertikopoulos, Bruno Lecouat, Houssam Zenati, Chuan-Sheng Foo, Vijay Chandrasekhar, and Georgios Piliouras. Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile. In International Conference on Learning Representations, 2018.
Lars Mescheder, Sebastian Nowozin, and Andreas Geiger. The numerics of GANs. Advances in Neural Information Processing Systems, 30, 2017.
Dmitriy Metelev, Alexander Rogozin, Alexander Gasnikov, and Dmitry Kovalev. Decentralized saddle-point problems with different constants of strong convexity and strong concavity. arXiv preprint arXiv:2206.00090, 2022.
Konstantin Mishchenko, Dmitry Kovalev, Egor Shulgin, Peter Richtárik, and Yura Malitsky. Revisiting stochastic extragradients. In International Conference on Artificial Intelligence and Statistics, pages 4573-4582. PMLR, 2020.
Aryan Mokhtari, Asuman Ozdaglar, and Sarath Pattathil. A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: Proximal point approach. In International Conference on Artificial Intelligence and Statistics, pages 1497-1507. PMLR, 2020.
Vaishnavh Nagarajan and J Zico Kolter. Gradient descent GAN optimization is locally stable. Advances in Neural Information Processing Systems, 30, 2017.
Arkadi Nemirovski. Prox-method with rate of convergence o (1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems. SIAM Journal on Optimization, 15(1):229-251, 2004.
Arkadi Nemirovski, Anatoli Juditsky, Guanghui Lan, and Alexander Shapiro. Robust stochastic approximation approach to stochastic programming. SIAM Journal on Optimization, 19:1574-1609, 2009.
Yurii Nesterov. Introductory lectures on convex optimization: A basic course, volume 87. Springer Science & Business Media, 2004.
Yurii Nesterov and Laura Scriminali. Solving strongly monotone variational and quasi-variational inequalities. Discrete & Continuous Dynamical Systems, 31(4):1383, 2011.
Yuyuan Ouyang and Yangyang Xu. Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems. Mathematical Programming, 185(1-2):1-35, 2021.
Brendan O'donoghue and Emmanuel Candes. Adaptive restart for accelerated gradient schemes. Foundations of computational mathematics, 15(3):715-732, 2015.
Hassan Rafique, Mingrui Liu, Qihang Lin, and Tianbao Yang. Weakly-convex-concave min-max optimization: provable algorithms and applications in machine learning. Optimization Methods and Software, pages 1-35, 2021.
James Renegar and Benjamin Grimmer. A simple nearly optimal restart scheme for speeding up first-order methods. Foundations of Computational Mathematics, 22(1):211-256, 2022.
Vincent Roulet and Alexandre d'Aspremont. Sharpness, restart and acceleration. Advances in Neural Information Processing Systems, 30, 2017.
Ernest K Ryu, Kun Yuan, and Wotao Yin. Ode analysis of stochastic gradient methods with optimism and anchoring for minimax problems. arXiv preprint arXiv:1905.10899, 2019.