Optimization Algorithms on Matrix Manifolds, 2008. ,
Hessian Riemannian gradient flows in convex programming, SIAM Journal on Control and Optimization, vol.43, issue.2, pp.477-501, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-01928141
A universal algorithm for variational inequalities adaptive to smoothness and noise, COLT '19: Proceedings of the 32nd Annual Conference on Learning Theory, 2019. ,
Quelques propriétés des opérateurs angle-bornés et n-cycliquement monotones, Israel Journal of Mathematics, vol.26, pp.137-150, 1977. ,
An Introduction to Riemann-Finsler Geometry, Number 200 in Graduate Texts in Mathematics, 2000. ,
Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01517477
A descent lemma beyond Lipschitz gradient continuity: First-order methods revisited and applications, Mathematics of Operations Research, vol.42, issue.2, pp.330-348, 2017. ,
First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems, SIAM Journal on Optimization, vol.28, issue.3, pp.2131-2151, 2018. ,
On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space, Journal of Mathematical Analysis and Applications, vol.61, issue.1, pp.159-164, 1977. ,
A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, vol.40, issue.1, pp.120-145, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00490826
Convergence analysis of a proximal-like minimization algorithm using Bregman functions, SIAM Journal on Optimization, vol.3, issue.3, pp.538-543, 1993. ,
Signal recovery by proximal forward-backward splitting, Multiscale Modeling and Simulation, vol.4, issue.4, pp.1168-1200, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00017649
Training GANs with optimism, ICLR '18: Proceedings of the 2018 International Conference on Learning Representations, 2018. ,
Finite-Dimensional Variational Inequalities and Complementarity Problems, 2003. ,
A variational inequality perspective on generative adversarial networks, ICLR '19: Proceedings of the 2019 International Conference on Learning Representations, 2019. ,
Negative momentum for improved game dynamics, AISTATS '19: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, 2019. ,
Generative adversarial nets, NIPS '14: Proceedings of the 27th International Conference on Neural Information Processing Systems, 2014. ,
Accelerated Bregman proximal gradient methods for relatively smooth convex optimization, 2018. ,
Extragradient method with variance reduction for stochastic variational inequalities, SIAM Journal on Optimization, vol.27, issue.2, pp.686-724, 2017. ,
Solving variational inequalities with stochastic mirror-prox algorithm, Stochastic Systems, vol.1, issue.1, pp.17-58, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00318043
Regularization techniques for learning with matrices, The Journal of Machine Learning Research, vol.13, pp.1865-1890, 2012. ,
Queueing Systems, vol.1, 1975. ,
The extragradient method for finding saddle points and other problems, Èkonom. i Mat. Metody, vol.12, pp.747-756, 1976. ,
Interaction matters: A note on non-asymptotic local convergence of generative adversarial networks, AISTATS '19: Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics, 2019. ,
Relative-continuity" for non-Lipschitz non-smooth convex optimization using stochastic (or deterministic) mirror descent, 2017. ,
Relatively-smooth convex optimization by first-order methods and applications, SIAM Journal on Optimization, vol.28, issue.1, pp.333-354, 2018. ,
Projected reflected gradient methods for monotone variational inequalities, SIAM Journal on Optimization, vol.25, issue.1, pp.502-520, 2015. ,
Learning in games via reinforcement and regularization, Mathematics of Operations Research, vol.41, issue.4, pp.1297-1324, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01073491
Riemannian game dynamics, Journal of Economic Theory, vol.177, pp.315-364, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01382281
On the convergence of gradient-like flows with noisy gradient input, SIAM Journal on Optimization, vol.28, issue.1, pp.163-197, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01404586
Learning in games with continuous action sets and unknown payoff functions, Mathematical Programming, vol.173, issue.1-2, pp.465-507, 2019. ,
Distributed stochastic optimization via matrix exponential learning, IEEE Trans. Signal Process, vol.65, issue.9, pp.2277-2290, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01382285
Cycles in adversarial regularized learning, SODA '18: Proceedings of the 29th annual ACM-SIAM Symposium on Discrete Algorithms, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01643338
Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile, ICLR '19: Proceedings of the 2019 International Conference on Learning Representations, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02111937
A unified analysis of extra-gradient and optimistic gradient methods for saddle point problems: proximal point approach, 2019. ,
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, vol.15, issue.1, pp.229-251, 2004. ,
Robust stochastic approximation approach to stochastic programming, SIAM Journal on Optimization, vol.19, issue.4, pp.1574-1609, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00976649
Dual extrapolation and its applications to solving variational inequalities and related problems, Mathematical Programming, vol.109, issue.2, pp.319-344, 2007. ,
Primal-dual subgradient methods for convex problems, Mathematical Programming, vol.120, issue.1, pp.221-259, 2009. ,
, Algorithmic Game Theory, 2007.
Conditional image synthesis with auxiliary classifier GANs, 2016. ,
Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, Journal of Mathematical Analysis and Applications, vol.72, issue.2, pp.383-390, 1979. ,
Online learning with predictable sequences, COLT '13: Proceedings of the 26th Annual Conference on Learning Theory, 2013. ,
Optimization, learning, and games with predictable sequences, NIPS '13: Proceedings of the 26th International Conference on Neural Information Processing Systems, 2013. ,
A New Mathematical Framework for the Study of Linkage and Selection. Number 211 in Memoirs of the, 1979. ,
Optimization for Machine Learning, 2012. ,
Formes bilineaires coercitives sur les ensembles convexes. Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 1964. ,
Some theoretical aspects of road traffic research, Proceedings of the Institute of Civil Engineers, Part II, vol.1, pp.325-378, 1952. ,
Stabilizing adversarial nets with prediction methods, ICLR '18: Proceedings of the 2018 International Conference on Learning Representations, 2018. ,