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@article{manopt,
author = {Boumal, N. and Mishra, B. and Absil, P.-A. and Sepulchre, R.},
title = {{M}anopt, a {M}atlab Toolbox for Optimization on Manifolds},
journal = {Journal of Machine Learning Research},
year = {2014},
volume = {15},
pages = {1455--1459},
url = {http://www.manopt.org}
}
@inproceedings{ge2016efficient,
title={Efficient algorithms for large-scale generalized eigenvector computation and canonical correlation analysis},
author={Ge, Rong and Jin, Chi and Netrapalli, Praneeth and Sidford, Aaron and others},
booktitle={International Conference on Machine Learning},
pages={2741--2750},
year={2016}
}
@article{Goodfellow2014,
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{Xu}, B. and {Warde-Farley}, D. and {Ozair}, S. and {Courville}, A. and
{Bengio}, Y.},
url = {https://arxiv.org/abs/1406.2661},
title = "{Generative Adversarial Networks}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1406.2661},
primaryClass = "stat.ML",
keywords = {Statistics - Machine Learning, Computer Science - Machine Learning},
year = 2014,
month = jun,
adsurl = {http://adsabs.harvard.edu/abs/2014arXiv1406.2661G},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Ilyas2017,
author = {{Ilyas}, Andrew and {Jalal}, Ajil and {Asteri}, Eirini and {Daskalakis},
Constantinos and {Dimakis}, Alexandros G.},
title = "{The Robust Manifold Defense: Adversarial Training using Generative Models}",
journal = {arXiv e-prints},
keywords = {Computer Science - Computer Vision and Pattern Recognition, Computer Science - Cryptography and Security, Computer Science - Machine Learning, Statistics - Machine Learning},
year = 2017,
month = Dec,
eid = {arXiv:1712.09196},
pages = {arXiv:1712.09196},
archivePrefix = {arXiv},
eprint = {1712.09196},
primaryClass = {cs.CV},
adsurl = {https://ui.adsabs.harvard.edu/\#abs/2017arXiv171209196I},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{Szegedy2013,
author = {{Szegedy}, Christian and {Zaremba}, Wojciech and {Sutskever}, Ilya and
{Bruna}, Joan and {Erhan}, Dumitru and {Goodfellow}, Ian and
{Fergus}, Rob},
title = "{Intriguing properties of neural networks}",
journal = {arXiv e-prints},
keywords = {Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning, Computer Science - Neural and Evolutionary Computing},
year = 2013,
month = Dec,
eid = {arXiv:1312.6199},
pages = {arXiv:1312.6199},
archivePrefix = {arXiv},
eprint = {1312.6199},
primaryClass = {cs.CV},
adsurl = {https://ui.adsabs.harvard.edu/\#abs/2013arXiv1312.6199S},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{tepper2018clustering,
title={Clustering is semidefinitely not that hard: Nonnegative SDP for manifold disentangling},
author={Tepper, Mariano and Sengupta, Anirvan M and Chklovskii, Dmitri},
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volume={19},
number={82},
year={2018}
}
@article{beck2009fast,
title={A fast iterative shrinkage-thresholding algorithm for linear inverse problems},
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year={2009},
publisher={SIAM}
}
@article{tibshirani1996regression,
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}
@book{bauschke2011convex,
title={Convex analysis and monotone operator theory in Hilbert spaces},
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volume={408},
year={2011},
publisher={Springer}
}
@article{waldspurger2018rank,
title={Rank optimality for the Burer-Monteiro factorization},
author={Waldspurger, Ir{\`e}ne and Waters, Alden},
journal={arXiv preprint arXiv:1812.03046},
year={2018}
}
@inproceedings{jaggi2013revisiting,
title={Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization.},
author={Jaggi, Martin},
booktitle={ICML (1)},
pages={427--435},
year={2013}
}
@inproceedings{nesterov1983method,
title={A method for solving the convex programming problem with convergence rate O (1/k\^{} 2)},
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@inproceedings{raghavendra2008optimal,
title={Optimal algorithms and inapproximability results for every CSP?},
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pages={245--254},
year={2008},
organization={ACM}
}
@online{xiao2017/online,
author = {Han Xiao and Kashif Rasul and Roland Vollgraf},
title = {Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms},
date = {2017-08-28},
year = {2017},
eprintclass = {cs.LG},
eprinttype = {arXiv},
eprint = {cs.LG/1708.07747},
}
@article{cartis2011evaluation,
title={On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming},
author={Cartis, Coralia and Gould, Nicholas IM and Toint, Philippe L},
journal={SIAM Journal on Optimization},
volume={21},
number={4},
pages={1721--1739},
year={2011},
publisher={SIAM}
}
@article{bolte2017error,
title={From error bounds to the complexity of first-order descent methods for convex functions},
author={Bolte, J{\'e}r{\^o}me and Nguyen, Trong Phong and Peypouquet, Juan and Suter, Bruce W},
journal={Mathematical Programming},
volume={165},
number={2},
pages={471--507},
year={2017},
publisher={Springer}
}
@article{obozinski2011group,
title={Group lasso with overlaps: the latent group lasso approach},
author={Obozinski, Guillaume and Jacob, Laurent and Vert, Jean-Philippe},
journal={arXiv preprint arXiv:1110.0413},
year={2011}
}
@article{tran2018smooth,
title={A smooth primal-dual optimization framework for nonsmooth composite convex minimization},
author={Tran-Dinh, Quoc and Fercoq, Olivier and Cevher, Volkan},
journal={SIAM Journal on Optimization},
volume={28},
number={1},
pages={96--134},
year={2018},
publisher={SIAM}
}
@article{tran2018adaptive,
title={An Adaptive Primal-Dual Framework for Nonsmooth Convex Minimization},
author={Tran-Dinh, Quoc and Alacaoglu, Ahmet and Fercoq, Olivier and Cevher, Volkan},
journal={arXiv preprint arXiv:1808.04648},
year={2018}
}
@article{candes2008introduction,
title={An introduction to compressive sampling},
author={Cand{\`e}s, Emmanuel J and Wakin, Michael B},
journal={IEEE signal processing magazine},
volume={25},
number={2},
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year={2008},
publisher={IEEE}
}
@article{chen2001atomic,
title={Atomic decomposition by basis pursuit},
author={Chen, Scott Shaobing and Donoho, David L and Saunders, Michael A},
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year={2001},
publisher={SIAM}
}
@article{flores2012complete,
title={A complete characterization of strong duality in nonconvex optimization with a single constraint},
author={Flores-Baz{\'a}n, Fabi{\'a}n and Flores-Baz{\'a}n, Fernando and Vera, Cristi{\'a}n},
journal={Journal of Global Optimization},
volume={53},
number={2},
pages={185--201},
year={2012},
publisher={Springer}
}
@article{dai2002convergence,
title={Convergence properties of the BFGS algoritm},
author={Dai, Yu-Hong},
journal={SIAM Journal on Optimization},
volume={13},
number={3},
pages={693--701},
year={2002},
publisher={SIAM}
}
@article{yang2015sdpnal,
title={SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints},
author={Yang, Liuqin and Sun, Defeng and Toh, Kim-Chuan},
journal={Mathematical Programming Computation},
volume={7},
number={3},
pages={331--366},
year={2015},
publisher={Springer}
}
@article{mascarenhas2004bfgs,
title={The BFGS method with exact line searches fails for non-convex objective functions},
author={Mascarenhas, Walter F},
journal={Mathematical Programming},
volume={99},
number={1},
pages={49--61},
year={2004},
publisher={Springer}
}
@inproceedings{bhojanapalli2016dropping,
title={Dropping convexity for faster semi-definite optimization},
author={Bhojanapalli, Srinadh and Kyrillidis, Anastasios and Sanghavi, Sujay},
booktitle={Conference on Learning Theory},
pages={530--582},
year={2016}
}
@article{arora2018compressed,
title={A compressed sensing view of unsupervised text embeddings, bag-of-n-grams, and LSTMs},
author={Arora, Sanjeev and Khodak, Mikhail and Saunshi, Nikunj and Vodrahalli, Kiran},
year={2018}
}
@article{shi2017penalty,
title={Penalty dual decomposition method for nonsmooth nonconvex optimization},
author={Shi, Qingjiang and Hong, Mingyi and Fu, Xiao and Chang, Tsung-Hui},
journal={arXiv preprint arXiv:1712.04767},
year={2017}
}
@article{fernandez2012local,
title={Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition},
author={Fern{\'a}ndez, Dami{\'a}n and Solodov, Mikhail V},
journal={SIAM Journal on Optimization},
volume={22},
number={2},
pages={384--407},
year={2012},
publisher={SIAM}
}
@article{bolte2018nonconvex,
title={Nonconvex Lagrangian-based optimization: monitoring schemes and global convergence},
author={Bolte, J{\'e}r{\^o}me and Sabach, Shoham and Teboulle, Marc},
journal={Mathematics of Operations Research},
year={2018},
publisher={INFORMS}
}
@article{nouiehed2018convergence,
title={Convergence to Second-Order Stationarity for Constrained Non-Convex Optimization},
author={Nouiehed, Maher and Lee, Jason D and Razaviyayn, Meisam},
journal={arXiv preprint arXiv:1810.02024},
year={2018}
}
@article{cartis2018optimality,
title={Optimality of orders one to three and beyond: characterization and evaluation complexity in constrained nonconvex optimization},
author={Cartis, Coralia and Gould, Nicholas IM and Toint, Ph L},
journal={Journal of Complexity},
year={2018},
publisher={Elsevier}
}
@article{nesterov2009primal,
title={Primal-dual subgradient methods for convex problems},
author={Nesterov, Yurii},
journal={Mathematical programming},
volume={120},
number={1},
pages={221--259},
year={2009},
publisher={Springer}
}
@inproceedings{yurtsever2015universal,
title={A universal primal-dual convex optimization framework},
author={Yurtsever, Alp and Dinh, Quoc Tran and Cevher, Volkan},
booktitle={Advances in Neural Information Processing Systems},
pages={3150--3158},
year={2015}
}
@article{yurtsever2018conditional,
title={A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming},
author={Yurtsever, Alp and Fercoq, Olivier and Locatello, Francesco and Cevher, Volkan},
journal={arXiv preprint arXiv:1804.08544},
year={2018}
}
@article{bertsekas1976penalty,
title={On penalty and multiplier methods for constrained minimization},
author={Bertsekas, Dimitri P},
journal={SIAM Journal on Control and Optimization},
volume={14},
number={2},
pages={216--235},
year={1976},
publisher={SIAM}
}
@article{powell1969method,
title={A method for nonlinear constraints in minimization problems},
author={Powell, Michael JD},
journal={Optimization},
pages={283--298},
year={1969},
publisher={Academic Press}
}
@book{bertsekas2014constrained,
title={Constrained optimization and Lagrange multiplier methods},
author={Bertsekas, Dimitri P},
year={2014},
publisher={Academic press}
}
@inproceedings{kulis2007fast,
title={Fast low-rank semidefinite programming for embedding and clustering},
author={Kulis, Brian and Surendran, Arun C and Platt, John C},
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year={2007}
}
@article{xu2017inexact,
title={Iteration complexity of inexact augmented Lagrangian methods for constrained convex programming},
author={Xu, Yangyang},
journal={arXiv preprint arXiv:1711.05812v2},
year={2017}
}
@article{nedelcu2014computational,
title={Computational complexity of inexact gradient augmented Lagrangian methods: application to constrained MPC},
author={Nedelcu, Valentin and Necoara, Ion and Tran-Dinh, Quoc},
journal={SIAM Journal on Control and Optimization},
volume={52},
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year={2014},
publisher={SIAM}
}
@article{pataki1998rank,
title={On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues},
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@article{cartis2012complexity,
title={Complexity bounds for second-order optimality in unconstrained optimization},
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volume={28},
number={1},
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year={2012},
publisher={Elsevier}
}
@article{ghadimi2016accelerated,
title={Accelerated gradient methods for nonconvex nonlinear and stochastic programming},
author={Ghadimi, Saeed and Lan, Guanghui},
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volume={156},
number={1-2},
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year={2016},
publisher={Springer}
}
@article{boumal2014manopt,
Author = {Boumal, Nicolas and Mishra, Bamdev and Absil, P-A and Sepulchre, Rodolphe},
Journal = {The Journal of Machine Learning Research},
Number = {1},
Pages = {1455--1459},
Publisher = {JMLR. org},
Title = {Manopt, a Matlab toolbox for optimization on manifolds},
Volume = {15},
Year = {2014}}
@article{boumal2016global,
Author = {Boumal, Nicolas and Absil, P-A and Cartis, Coralia},
Journal = {arXiv preprint arXiv:1605.08101},
Title = {Global rates of convergence for nonconvex optimization on manifolds},
Year = {2016}}
@inproceedings{boumal2016non,
Author = {Boumal, Nicolas and Voroninski, Vlad and Bandeira, Afonso},
Booktitle = {Advances in Neural Information Processing Systems},
Pages = {2757--2765},
Title = {The non-convex Burer-Monteiro approach works on smooth semidefinite programs},
Year = {2016}}
@article{davis2011university,
Author = {Davis, Timothy A and Hu, Yifan},
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Year = {2011}
}
@article{clason2018acceleration,
Author = {Clason, Christian and Mazurenko, Stanislav and Valkonen, Tuomo},
Journal = {arXiv preprint arXiv:1802.03347},
Title = {Acceleration and global convergence of a first-order primal--dual method for nonconvex problems},
Year = {2018}}
@article{chambolle2011first,
Author = {Chambolle, Antonin and Pock, Thomas},
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Publisher = {Springer},
Title = {A first-order primal-dual algorithm for convex problems with applications to imaging},
Volume = {40},
Year = {2011}}
@article{tran2018smooth,
Author = {Tran-Dinh, Quoc and Fercoq, Olivier and Cevher, Volkan},
Journal = {SIAM Journal on Optimization},
Number = {1},
Pages = {96--134},
Publisher = {SIAM},
Title = {A smooth primal-dual optimization framework for nonsmooth composite convex minimization},
Volume = {28},
Year = {2018}}
@article{bhojanapalli2018smoothed,
Author = {Bhojanapalli, Srinadh and Boumal, Nicolas and Jain, Prateek and Netrapalli, Praneeth},
Journal = {arXiv preprint arXiv:1803.00186},
Title = {Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form},
Year = {2018}}
@inproceedings{jin2017escape,
Author = {Jin, Chi and Ge, Rong and Netrapalli, Praneeth and Kakade, Sham M and Jordan, Michael I},
Booktitle = {International Conference on Machine Learning},
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Title = {How to Escape Saddle Points Efficiently},
Year = {2017}}
@article{birgin2016evaluation,
title={Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models},
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}
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Title = {Linearized admm for non-convex non-smooth optimization with convergence analysis},
Year = {2017}}
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Year = {2016}
}
@book{bertsekas1999nonlinear,
title={Nonlinear programming},
author={Bertsekas, Dimitri P}
}
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Date-Added = {2017-10-26 15:22:37 +0000},
Date-Modified = {2017-10-26 15:30:53 +0000},
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title = {Compressed {Sensing} using {Generative} {Models}},
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keywords = {Statistics - Machine Learning, Computer Science - Machine
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}
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@inproceedings{Samangouei2018,
title={Defense-{GAN}: Protecting Classifiers Against Adversarial Attacks Using Generative Models},
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booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=BkJ3ibb0-},
}
@ARTICLE{Kingma2014,
author = {{Kingma}, Diederik P. and {Ba}, Jimmy},
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eid = {arXiv:1412.6980},
pages = {arXiv:1412.6980},
archivePrefix = {arXiv},
eprint = {1412.6980},
primaryClass = {cs.LG},
adsurl = {https://ui.adsabs.harvard.edu/\#abs/2014arXiv1412.6980K},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@inproceedings{Madry2018,
title={Towards Deep Learning Models Resistant to Adversarial Attacks},
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booktitle={International Conference on Learning Representations},
year={2018},
url={https://openreview.net/forum?id=rJzIBfZAb},
}
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doi = {10.1145/1390156.1390191},
acmid = {1390191},
publisher = {ACM},
address = {New York, NY, USA},
}
@article{Kingma2013,
author = {{Kingma}, Diederik P and {Welling}, Max},
title = "{Auto-Encoding Variational Bayes}",
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year = 2013,
month = Dec,
eid = {arXiv:1312.6114},
pages = {arXiv:1312.6114},
archivePrefix = {arXiv},
eprint = {1312.6114},
primaryClass = {stat.ML},
adsurl = {https://ui.adsabs.harvard.edu/\#abs/2013arXiv1312.6114K},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
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