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In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint.
Incorporating second-order functional knowledge for better option pricing
Charles Dugas, Yoshua Bengio, François Bélisle, Claude Nadeau, and René Garcia · 1920
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Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de problèmes de dirichlet non linéaires
R. Glowinski and A. Marroco · 1975
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On penalty and multiplier methods for constrained minimization
Dimitri P Bertsekas · 1976
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A dual algorithm for the solution of nonlinear variational problems via finite element approximation
Daniel Gabay and Bertrand Mercier · 1976
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities
BS He, Hai Yang, and SL Wang · 2000
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Efficient projections onto the l1-ball for learning in high dimensions
John Duchi, Shai Shalev-Shwartz, Yoram Singer, and Tushar Chandra · 2008
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Fast global convergence rates of gradient methods for high-dimensional statistical recovery
Alekh Agarwal, Sahand Negahban, and Martin J Wainwright · 2010
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MNIST handwritten digit database
Yann LeCun and Corinna Cortes · 2010
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Distributed optimization and statistical learning via the alternating direction method of multipliers
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein, et al · 2011
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A complete characterization of strong duality in nonconvex optimization with a single constraint
Fabián Flores-Bazán, Fernando Flores-Bazán, and Cristián Vera · 2012
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A unified framework for high-dimensional analysis of
Sahand N Negahban, Pradeep Ravikumar, Martin J Wainwright, Bin Yu, et al · 2012
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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The convergence guarantees of a non-convex approach for sparse recovery
Laming Chen and Yuantao Gu · 2014
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A Course in Mathematical Analysis , volume 1
D. J. H. Garling · 2014
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Generative Adversarial Networks
I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Adam: A Method for Stochastic Optimization
Diederik P. Kingma and Jimmy Ba · 2014
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Proximal algorithms
Neal Parikh, Stephen Boyd, et al · 2014
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Stochastic backpropagation and approximate inference in deep generative models
Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra · 2014
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Fast and accurate deep network learning by exponential linear units (elus)
Djork-Arné Clevert, Thomas Unterthiner, and Sepp Hochreiter · 2015
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New analysis of manifold embeddings and signal recovery from compressive measurements
Armin Eftekhari and Michael B Wakin · 2015
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Deep Residual Learning for Image Recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Deep learning face attributes in the wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
A. Radford, L. Metz, and S. Chintala · 2015
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Empirical Evaluation of Rectified Activations in Convolutional Network
Bing Xu, Naiyan Wang, Tianqi Chen, and Mu Li · 2015
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Evaluation complexity for nonlinear constrained optimization using unscaled kkt conditions and high-order models
Ernesto G Birgin, JL Gardenghi, José Mario Martínez, SA Santos, and Ph L Toint · 2016
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Infogan: Interpretable representation learning by information maximizing generative adversarial nets
Xi Chen, Yan Duan, Rein Houthooft, John Schulman, Ilya Sutskever, and Pieter Abbeel · 2016
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Training GANs with optimism
Constantinos Daskalakis, Andrew Ilyas, Vasilis Syrgkanis, and Haoyang Zeng · 2018
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Modeling sparse deviations for compressed sensing using generative models
Manik Dhar, Aditya Grover, and Stefano Ermon · 2018
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Phase retrieval under a generative prior
Paul Hand, Oscar Leong, and Vlad Voroninski · 2018
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Algorithmic Aspects of Inverse Problems Using Generative Models
C. Hegde · 2018
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Finding Mixed Nash Equilibria of Generative Adversarial Networks
Ya-Ping Hsieh, Chen Liu, and Volkan Cevher · 2018
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Memorization precedes generation: Learning unsupervised GANs with memory networks
Youngjin Kim, Minjung Kim, and Gunhee Kim · 2018
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Raja Giryes, Yonina C Eldar, Alex M Bronstein, and Guillermo Sapiro · 2016
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Linearized alternating direction method of multipliers for constrained nonconvex regularized optimization
Linbo Qiao, Bofeng Zhang, Jinshu Su, and Xicheng Lu · 2016
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Improved techniques for training gans
Tim Salimans, Ian Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, Xi Chen, and Xi Chen · 2016
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Square-root lasso with nonconvex regularization: An admm approach
Xinyue Shen, Laming Chen, Yuantao Gu, and Hing-Cheung So · 2016
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Wasserstein generative adversarial networks
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Compressed Sensing using Generative Models
Ashish Bora, Ajil Jalal, Eric Price, and Alexandros G. Dimakis · 2017
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What happens to a manifold under a bi-lipschitz map?
Armin Eftekhari and Michael B Wakin · 2017
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Are gans created equal? a large-scale study
Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet · 2018
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Invertibility of convolutional generative networks from partial measurements
Fangchang Ma, Ulas Ayaz, and Sertac Karaman · 2018
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2018
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Which training methods for GANs do actually converge?
Lars Mescheder, Andreas Geiger, and Sebastian Nowozin · 2018
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Foundations of Machine Learning
M. Mohri, A. Rostamizadeh, A. Talwalkar, and F. Bach · 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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Sharp time–data tradeoffs for linear inverse problems
Samet Oymak, Benjamin Recht, and Mahdi Soltanolkotabi · 2018
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Defense-GAN: Protecting classifiers against adversarial attacks using generative models
Pouya Samangouei, Maya Kabkab, and Rama Chellappa · 2018
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Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees
Viraj Shah and Chinmay Hegde · 2018
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Correction by Projection: Denoising Images with Generative Adversarial Networks
Subarna Tripathi, Zachary C. Lipton, and Truong Q. Nguyen · 2018
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Deep image prior
Dmitry Ulyanov, Andrea Vedaldi, and Victor S. Lempitsky · 2018
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Large scale GAN training for high fidelity natural image synthesis
Andrew Brock, Jeff Donahue, and Karen Simonyan · 2019
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Adversarial audio synthesis
Chris Donahue, Julian McAuley, and Miller Puckette · 2019
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GANSynth: Adversarial neural audio synthesis
Jesse Engel, Kumar Krishna Agrawal, Shuo Chen, Ishaan Gulrajani, Chris Donahue, and Adam Roberts · 2019
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Negative momentum for improved game dynamics
Gauthier Gidel, Reyhane Askari Hemmat, Mohammad Pezeshki, Rémi Le Priol, Gabriel Huang, Simon Lacoste-Julien, and Ioannis Mitliagkas · 2019
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Deep denoising: Rate-optimal recovery of structured signals with a deep prior, 2019
Reinhard Heckel, Wen Huang, Paul Hand, and Vladislav Voroninski · 2019
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