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We study constrained comonotone min-max optimization, a structured class of nonconvex-nonconcave min-max optimization problems, and their generalization to comonotone inclusion.
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Finite-Dimensional Variational Inequalities and Complementarity Problems
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Proximal methods for cohypomonotone operators
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Prox-method with rate of convergence O (1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
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Dual extrapolation and its applications to solving variational inequalities and related problems
Nesterov, Y · 2007
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Ben-Tal, A., El Ghaoui, L., and Nemirovski, A · 2009
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Bauschke, H. H. and Combettes, P. L · 2011
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Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y · 2014
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On the convergence properties of non-euclidean extragradient methods for variational inequalities with generalized monotone operators
Dang, C. D. and Lan, G · 2015
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Primer on monotone operator methods
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Wasserstein Generative Adversarial Networks
Arjovsky, M., Chintala, S., and Bottou, L · 2017
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Convex Analysis and Monotone Operator Theory in Hilbert Spaces
Bauschke, H. H., Combettes, P. L., Bauschke, H. H., and Combettes, P. L · 2017
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Stochastic variance reduction methods for policy evaluation
Du, S. S., Chen, J., Li, L., Xiao, L., and Zhou, D · 2017
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Towards deep learning models resistant to adversarial attacks
Madry, A., Makelov, A., Schmidt, L., Tsipras, D., and Vladu, A · 2017
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Stochastic mirror descent in variationally coherent optimization problems
Zhou, Z., Mertikopoulos, P., Bambos, N., Boyd, S., and Glynn, P. W · 2017
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Sbeed: Convergent reinforcement learning with nonlinear function approximation
Dai, B., Shaw, A., Li, L., Xiao, L., He, N., Liu, Z., Chen, J., and Song, L · 2018
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Liu, M., Mroueh, Y., Ross, J., Zhang, W., Cui, X., Das, P., and Yang, T · 2019
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Halpern iteration for near-optimal and parameter-free monotone inclusion and strong solutions to variational inequalities
Diakonikolas, J · 2020
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Golden ratio algorithms for variational inequalities
Malitsky, Y · 2020
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Song, C., Zhou, Z., Zhou, Y., Jiang, Y., and Ma, Y · 2020
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Generalized monotone operators and their averaged resolvents
Extragradient method: 𝒪 ( 1 / k ) \mathcal{O}(1/k) last-iterate convergence for monotone variational inequalities and connections with cocoercivity
Gorbunov, E., Loizou, N., and Gidel, G · 2022
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On the proximal point algorithm and its halpern-type variant for generalized monotone operators in hilbert space
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