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We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics.
An algorithm for quadratic programming
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A method for unconstrained convex minimization problem with the rate of convergence O ( 1 / k 2 ) (1/k^{2})
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Dual gauge programs, with applications to quadratic programming and the minimum-norm problem
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On an approach to the construction of optimal methods of minimization of smooth convex functions
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Convex analysis and minimization algorithms
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Convex analysis
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Game theory, on-line prediction and boosting
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Strongly convex analysis
Polovinkin, E. S · 1996
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Variational analysis
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A modified forward-backward splitting method for maximal monotone mappings
Tseng, P · 2000
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Convex analysis and optimization
Bertsekas, D. P., Nedic, A. & Ozdaglar, A. E · 2003
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Introductory lectures on convex optimization: A basic course
Nesterov, Y · 2004
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Convex optimization
Boyd, S. & Vandenberghe, L · 2004
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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
Nemirovski, A · 2004
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On the generalization ability of on-line learning algorithms
Cesa-Bianchi, N., Conconi, A. & Gentile, C · 2004
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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
Nemirovski, A · 2004
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Smooth minimization of nonsmooth functions
Nesterov, Y · 2005
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Interior projection-like methods for monotone variational inequalities
Auslender, A. & Teboulle, M · 2005
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Efficient algorithms for online decision problems
Kalai, A. & Vempala, S · 2005
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Convex analysis and nonlinear optimization theory and examples
Borwein, J. & Lewis, A. S · 2006
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Dual extrapolation and its applications to solving variational inequalities and related problems
Nesterov, Y · 2007
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Online learning: Theory, algorithms, and applications
Shalev-Shwartz, S · 2007
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Dual extrapolation and its applications to solving variational inequalities and related problems
Nesterov, Y · 2007
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An efficient primal-dual hybrid gradient algorithm for total variation image restoration
Zhu, M. & Chan, T · 2008
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On accelerated proximal gradient methods for convex-concave optimization (2008)
Tseng, P · 2008
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Coresets, sparse greedy approximation, and the frank-wolfe algorithm
Clarkson, K · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
Beck, A. & Teboulle, M · 2009
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On the duality of strong convexity and strong smoothness: Learning applications and matrix regularization
Kakade, S. M., Shalev-shwartz, S. & Tewari, A · 2009
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Subgradient methods for saddle-point problems
Nedić, A. & Ozdaglar, A · 2009
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An algorithm for minimizing the mumford-shah functional
Pock, T., Cremers, D., Bischof, H. & Chambolle, A · 2009
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A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science
Esser, E., Zhang, X. & Chan, T. F · 2010
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Dual averaging methods for regularized stochastic learning and online optimization
Xiao, L · 2010
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Solving variational inequalities with stochastic mirror-prox algorithm
Juditsky, A., Nemirovski, A. & Tauvel, C · 2011
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A first-order primal-dual algorithm for convex problems with applications to imaging
Chambolle, A. & Pock, T · 2011
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What is a fenchel conjugate?
Bauschke, H. H. & Lucet, Y · 2012
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Online optimization with gradual variations
Chiang, C.-K. et al · 2012
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Online to offline conversions, universality and adaptive minibatch sizes
Levy, K · 2017
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Dissipativity theory for nesterov’s accelerated method
Hu, B. & Lessard, L · 2017
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Linear coupling: An ultimate unification of gradient and mirror descent
Allen-Zhu, Z. & Orecchia, L · 2017
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Integration methods and optimization algorithms
Scieur, D., Roulet, V., Bach, F. & d’Aspremont, A · 2017
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An optimal randomized incremental gradient method
Lan, G. & Zhou, Y · 2017
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Faster rates for convex-concave games
Abernethy, J., Levy, K., Lai, K. & Wang, J.-K · 2018
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Trading regret for efficiency: online convex optimization with long term constraints
Mahdavi, M., Jin, R. & Yang, T · 2012
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Online learning and online convex optimization
Shalev-Shwartz, S. et al · 2012
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Smoothing and first order methods: A unified framework
Beck, A. & Teboulle, M · 2012
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Optimization, learning, and games with predictable sequences
Rakhlin, A. & Sridharan, K · 2013
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Online learning with predictable sequences
Rakhlin, A. & Sridharan, K · 2013
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Revisiting frank-wolfe: Projection-free sparse convex optimization
Jaggi, M · 2013
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Acceleration through optimistic no-regret dynamics
Wang, J.-K. & Abernethy, J · 2018
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Primal–dual algorithms for convex optimization via regret minimization
Ho-Nguyen, N. & Kılınç-Karzan, F · 2018
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Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile
Mertikopoulos, P. et al · 2018
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Training gans with optimism
Daskalakis, C., Ilyas, A., Syrgkanis, V. & Zeng, H · 2018
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An optimal first order method based on optimal quadratic averaging
Drusvyatskiy, D., Fazel, M. & Roy, S · 2018
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Accelerated extra-gradient descent: A novel accelerated first-order method
Diakonikolas1, J. & Orecchia, L · 2018
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Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity
Attouch, H., Chbani, Z., Peypouquet, J. & Redont, P · 2018
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Relatively-smooth convex optimization by first-order methods and applications
Lu, H., Freund, R. M. & Nesterov, Y · 2018
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Convergence rates of proximal gradient methods via the convex conjugate
Gutman, D. H. & Pena, J. F · 2019
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Exploiting problem structure in optimization under uncertainty via online convex optimization
Ho-Nguyen, N. & Kılınç-Karzan, F · 2019
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A modern introduction to online learning
Orabona, F · 2019
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Blended conditonal gradients
Braun, G., Pokutta, S., Tu, D. & Wright, S · 2019
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On the convergence of single-call stochastic extra-gradient methods
Hsieh, Y.-G., Iutzeler, F., Malick, J. & Mertikopoulos, P · 2019
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A variational inequality perspective on generative adversarial networks
Gidel, G., Berard, H., Vignoud, G., Vincent, P. & Lacoste-Julien, S · 2019
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Anytime online-to-batch, optimism and acceleration
Cutkosky, A · 2019
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The approximate duality gap technique: A unified theory of first-order methods
Diakonikolas, J. & Orecchia, L · 2019
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Stochastic frank-wolfe for constrained finite-sum minimization
Négiar, G. et al · 2020
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Golden ratio algorithms for variational inequalities
Malitsky, Y · 2020
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Generalized stochastic frankwolfe algorithm with stochastic “substitute” gradient for structured convex optimization
Lu, H. & Freund, R. M · 2020
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Convergence rate of O(1/k) for optimistic gradient and extragradient methods in smooth convex-concave saddle point problems
Mokhtari, A., Ozdaglar, A. E. & Pattathil, S · 2020
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Training gans with centripetal acceleration
Peng, W., Dai, Y.-H., Zhang, H. & Cheng, L · 2020
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First-order and stochastic optimization methods for machine learning
Lan, G · 2020
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Curvature of feasible sets in offline and online optimization
Molinaro, M · 2020
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Relative lipschitzness in extragradient methods and a direct recipe for acceleration
Cohen, M. B., Sidford, A. & Tian, K · 2021
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