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We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness.
Monotone (nonlinear) operators in hilbert space
George J Minty et al · 1962
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Variational inequalities
Guido Stampacchia · 1970
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The extragradient method for finding saddle points and other problems
G Korpelevich · 1976
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An introduction to variational inequalities and their applications , volume 31
David Kinderlehrer and Guido Stampacchia · 1980
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Problem complexity and method efficiency in Optimization
Arkadi Nemirovski and David Berkovich Yudin · 1983
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Interior-point polynomial algorithms in convex programming , volume 13
Yurii Nesterov and Arkadi Nemirovski · 1994
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On the stampacchia and minty variational inequalities
Sándor Komlósi · 1999
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Prox-method with rate of convergence O ( 1 / t ) {O}(1/t) for variational inequalities with lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Arkadi Nemirovski · 2004
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Cubic regularization of Newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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Accelerating the cubic regularization of Newton’s method on convex problems
Yu Nesterov · 2008
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On accelerated proximal gradient methods for convex-concave optimization
Paul Tseng · 2008
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Estimate sequence methods: extensions and approximations
Michel Baes · 2009
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On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean
Renato DC Monteiro and Benar Fux Svaiter · 2010
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Iteration-complexity of a newton proximal extragradient method for monotone variational inequalities and inclusion problems
Renato DC Monteiro and Benar F Svaiter · 2012
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An accelerated hybrid proximal extragradient method for convex optimization and its implications to second-order methods
Renato DC Monteiro and Benar Fux Svaiter · 2013
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Finding approximate local minima faster than gradient descent
Naman Agarwal, Zeyuan Allen-Zhu, Brian Bullins, Elad Hazan, and Tengyu Ma · 2017
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The global rate of convergence for optimal tensor methods in smooth convex optimization
Alexander Gasnikov, Pavel Dvurechensky, Eduard Gorbunov, Dmitry Kovalev, Ahmed Mohhamed, Elena Chernousova, and César A. Uribe · 2018
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Global convergence to the equilibrium of gans using variational inequalities
Ian Gemp and Sridhar Mahadevan · 2018
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An optimal high-order tensor method for convex optimization
Bo Jiang, Haoyue Wang, and Shuzhong Zhang · 2018
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Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems
Yuyuan Ouyang and Yangyang Xu · 2018
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