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Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade.
On general minimax theorems
M. Sion · 1958
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Error bounds and convergence analysis of feasible descent methods: A general approach
Z.-Q. Luo and P. Tseng · 1993
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H. H. Bauschke and J. M. Borwein · 1996
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Optimization of conditional value-at-risk
R. T. Rockafellar and S. Uryasev · 2000
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On approximate solutions of systems of linear inequalities
A. J. Hoffman · 2003
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Modified Gauss-Newton scheme with worst case guarantees for global performance
Y. Nesterov · 2007
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Variational Analysis , volume 317 of Grundlehren der mathematischen Wissenschaften
R. T. Rockafellar and R. J.-B. Wets · 2009
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Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka-Łojasiewicz inequality
H. Attouch, J. Bolte, P. Redont, and A. Soubeyran · 2010
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Characterizations of Łojasiewicz inequalities and applications
J. Bolte, A. Daniilidis, O. Ley, and L. Mazet · 2010
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Robust linear least squares regression
J.-Y. Audibert and O. Catoni · 2011
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Theory and applications of robust optimization
D. Bertsimas, D. B. Brown, and C. Caramanis · 2011
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On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming
C. Cartis, N. I. M. Gould, and P. L. Toint · 2011
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Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
H. Attouch, J. Bolte, and B. F. Svaiter · 2013
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Kullback-Leibler divergence constrained distributionally robust optimization
Z. Hu and L. J. Hong · 2013
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Convex optimization: Algorithms and complexity
S. Bubeck · 2015
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Splitting methods with variable metric for Kurdyka-Łojasiewicz functions and general convergence rates
P. Frankel, G. Garrigos, and J. Peypouquet · 2015
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On convergence rates of linearized proximal algorithms for convex composite optimization with applications
Y. Hu, C. Li, and X. Yang · 2016
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A proximal method for composite minimization
A. S. Lewis and S. J. Wright · 2016
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Stochastic gradient methods for distributionally robust optimization with f f -divergences
H. Namkoong and J. C. Duchi · 2016
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A unified distributed algorithm for non-cooperative games
J.-S. Pang and M. Razaviyayn · 2016
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Minimizing the maximal loss: How and why
S. Shalev-Shwartz and Y. Wexler · 2016
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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From error bounds to the complexity of first-order descent methods for convex functions
J. Bolte, T. P. Nguyen, J. Peypouquet, and B. W. Suter · 2017
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A unified approach to error bounds for structured convex optimization problems
Z. Zhou and A. M.-C. So · 2017
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Error bounds, quadratic growth, and linear convergence of proximal methods
D. Drusvyatskiy and A. S. Lewis · 2018
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Calculus of the exponent of Kurdyka-Łojasiewicz inequality and its applications to linear convergence of first-order methods
G. Li and T. K. Pong · 2018
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Towards deep learning models resistant to adversarial attacks
A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu · 2018
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Hybrid block successive approximation for one-sided non-convex min-max problems: Algorithms and applications
S. Lu, I. Tsaknakis, M. Hong, and Y. Chen · 2020
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Nonconvex min-max optimization: Applications, challenges, and recent theoretical advances
M. Razaviyayn, T. Huang, S. Lu, M. Nouiehed, M. Sanjabi, and M. Hong · 2020
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A catalyst framework for minimax optimization
J. Yang, S. Zhang, N. Kiyavash, and N. He · 2020
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A proximal alternating direction method of multiplier for linearly constrained nonconvex minimization
J. Zhang and Z.-Q. Luo · 2020
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A single-loop smoothed gradient descent-ascent algorithm for nonconvex-concave min-max problems
J. Zhang, P. Xiao, R. Sun, and Z. Luo · 2020
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Certifying some distributional robustness with principled adversarial training
A. Sinha, H. Namkoong, and J. Duchi · 2018
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ℓ 1 \ell_{1} -regression with heavy-tailed distributions
L. Zhang and Z.-H. Zhou · 2018
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Stochastic model-based minimization of weakly convex functions
D. Davis and D. Drusvyatskiy · 2019
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Efficiency of minimizing compositions of convex functions and smooth maps
D. Drusvyatskiy and C. Paquette · 2019
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Agnostic federated learning
M. Mohri, G. Sivek, and A. T. Suresh · 2019
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Solving a class of non-convex min-max games using iterative first order methods
M. Nouiehed, M. Sanjabi, T. Huang, J. D. Lee, and M. Razaviyayn · 2019
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Regularization via mass transportation
S. Shafieezadeh-Abadeh, D. Kuhn, and P. M. Esfahani · 2019
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Z. Chen, Y. Zhou, T. Xu, and Y. Liang · 2021
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Generalised Lipschitz regularisation equals distributional robustness
Z. Cranko, Z. Shi, X. Zhang, R. Nock, and S. Kornblith · 2021
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The complexity of constrained min-max optimization
C. Daskalakis, S. Skoulakis, and M. Zampetakis · 2021
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Nonsmooth optimization using Taylor-like models: Error bounds, convergence, and termination criteria
D. Drusvyatskiy, A. D. Ioffe, and A. S. Lewis · 2021
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Efficient mirror descent ascent methods for nonsmooth minimax problems
F. Huang, X. Wu, and H. Huang · 2021
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Complexity lower bounds for nonconvex-strongly-concave min-max optimization
H. Li, Y. Tian, J. Zhang, and A. Jadbabaie · 2021
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Efficient search of first-order Nash equilibria in nonconvex-concave smooth min-max problems
D. M. Ostrovskii, A. Lowy, and M. Razaviyayn · 2021
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The complexity of nonconvex-strongly-concave minimax optimization
S. Zhang, J. Yang, C. Guzmán, N. Kiyavash, and N. He · 2021
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Modern Nonconvex Nondifferentiable Optimization
Y. Cui and J.-S. Pang · 2022
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Weakly-convex–concave min–max optimization: Provable algorithms and applications in machine learning
H. Rafique, M. Liu, Q. Lin, and T. Yang · 2022
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Frameworks and results in distributionally robust optimization
H. Rahimian and S. Mehrotra · 2022
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Faster single-loop algorithms for minimax optimization without strong concavity
J. Yang, A. Orvieto, A. Lucchi, and N. He · 2022
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Alternating proximal-gradient steps for (stochastic) nonconvex-concave minimax problems
R. I. Boţ and A. Böhm · 2023
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Linearized proximal algorithms with adaptive stepsizes for convex composite optimization with applications
Y. Hu, C. Li, J. Wang, X. Yang, and L. Zhu · 2023
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A unified single-loop alternating gradient projection algorithm for nonconvex–concave and convex–nonconcave minimax problems
Z. Xu, H. Zhang, Y. Xu, and G. Lan · 2023
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Wasserstein distributionally robust optimization and variation regularization
R. Gao, X. Chen, and A. J. Kleywegt · 2024
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Two-timescale gradient descent ascent algorithms for nonconvex minimax optimization
T. Lin, C. Jin, and M. Jordan · 2024
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