On lower iteration complexity bounds for the convex concave saddle point problems

[1]  Yurii Nesterov,et al.  Implementable tensor methods in unconstrained convex optimization , 2019, Mathematical Programming.

[2]  Yangyang Xu,et al.  Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems , 2018, Math. Program..

[3]  Yair Carmon,et al.  Lower bounds for finding stationary points II: first-order methods , 2017, Mathematical Programming.

[4]  Yuanhao Wang,et al.  Improved Algorithms for Convex-Concave Minimax Optimization , 2020, NeurIPS.

[5]  Michael I. Jordan,et al.  Near-Optimal Algorithms for Minimax Optimization , 2020, COLT.

[6]  Ioannis Mitliagkas,et al.  Accelerating Smooth Games by Manipulating Spectral Shapes , 2020, AISTATS.

[7]  Ioannis Mitliagkas,et al.  Linear Lower Bounds and Conditioning of Differentiable Games , 2019, ICML.

[8]  Michael I. Jordan,et al.  On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems , 2019, ICML.

[9]  Yongxin Chen,et al.  Hybrid Block Successive Approximation for One-Sided Non-Convex Min-Max Problems: Algorithms and Applications , 2019, IEEE Transactions on Signal Processing.

[10]  Michael I. Jordan,et al.  What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization? , 2019, ICML.

[11]  Aryan Mokhtari,et al.  A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach , 2019, AISTATS.

[12]  Yair Carmon,et al.  Lower bounds for finding stationary points I , 2017, Mathematical Programming.

[13]  Michael I. Jordan,et al.  Minmax Optimization: Stable Limit Points of Gradient Descent Ascent are Locally Optimal , 2019, ArXiv.

[14]  Weizhu Chen,et al.  DSCOVR: Randomized Primal-Dual Block Coordinate Algorithms for Asynchronous Distributed Optimization , 2017, J. Mach. Learn. Res..

[15]  Ohad Shamir,et al.  Oracle complexity of second-order methods for smooth convex optimization , 2017, Mathematical Programming.

[16]  Jason D. Lee,et al.  Solving Non-Convex Non-Concave Min-Max Games Under Polyak-Łojasiewicz Condition , 2018, ArXiv.

[17]  Yurii Nesterov,et al.  Lectures on Convex Optimization , 2018 .

[18]  Mingrui Liu,et al.  Solving Weakly-Convex-Weakly-Concave Saddle-Point Problems as Weakly-Monotone Variational Inequality , 2018 .

[19]  Mingrui Liu,et al.  Solving Weakly-Convex-Weakly-Concave Saddle-Point Problems as Successive Strongly Monotone Variational Inequalities , 2018 .

[20]  Naman Agarwal,et al.  Lower Bounds for Higher-Order Convex Optimization , 2017, COLT.

[21]  Shuzhong Zhang,et al.  First-Order Algorithms for Convex Optimization with Nonseparable Objective and Coupled Constraints , 2017 .

[22]  Léon Bottou,et al.  Wasserstein GAN , 2017, ArXiv.

[23]  Yangyang Xu,et al.  Accelerated First-Order Primal-Dual Proximal Methods for Linearly Constrained Composite Convex Programming , 2016, SIAM J. Optim..

[24]  Antonin Chambolle,et al.  On the ergodic convergence rates of a first-order primal–dual algorithm , 2016, Math. Program..

[25]  Daniel Kuhn,et al.  Distributionally Robust Logistic Regression , 2015, NIPS.

[26]  Yunmei Chen,et al.  An Accelerated Linearized Alternating Direction Method of Multipliers , 2014, SIAM J. Imaging Sci..

[27]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[28]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[29]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[30]  A. Juditsky,et al.  Solving variational inequalities with Stochastic Mirror-Prox algorithm , 2008, 0809.0815.

[31]  Yurii Nesterov,et al.  Dual extrapolation and its applications to solving variational inequalities and related problems , 2003, Math. Program..

[32]  Yurii Nesterov,et al.  Solving Strongly Monotone Variational and Quasi-Variational Inequalities , 2006 .

[33]  Arkadi Nemirovski,et al.  Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems , 2004, SIAM J. Optim..

[34]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[35]  Masao Fukushima,et al.  A globally convergent Newton method for solving strongly monotone variational inequalities , 1993, Math. Program..

[36]  Arkadi S. Nemirovsky,et al.  Information-based complexity of linear operator equations , 1992, J. Complex..

[37]  P. Marcotte,et al.  A note on a globally convergent Newton method for solving monotone variational inequalities , 1986 .

[38]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[39]  G. M. Korpelevich.  The extragradient method for finding saddle points and other problems , 1976 .

[40]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.