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@book{birgin2014practical,
title={Practical augmented Lagrangian methods for constrained optimization},
author={Birgin, Ernesto G and Mart\_nez, Jos{\^a} Mario},
volume={10},
year={2014},
publisher={SIAM}
}
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title={Constrained optimization and Lagrange Multiplier methods},
author={Bertsekas, Dimitri P},
journal={Computer Science and Applied Mathematics, Boston: Academic Press, 1982},
year={1982}
}
@inproceedings{karimi2016linear,
title={Linear convergence of gradient and proximal-gradient methods under the polyak-{\l}ojasiewicz condition},
author={Karimi, Hamed and Nutini, Julie and Schmidt, Mark},
booktitle={Joint European Conference on Machine Learning and Knowledge Discovery in Databases},
pages={795--811},
year={2016},
organization={Springer}
}
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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,
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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}
}
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{Fergus}, Rob},
title = "{Intriguing properties of neural networks}",
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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},
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year={2018}
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date = {2017-08-28},
year = {2017},
eprintclass = {cs.LG},
eprinttype = {arXiv},
eprint = {cs.LG/1708.07747},
}
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title={On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming},
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pages={1721--1739},
year={2011},
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title={From error bounds to the complexity of first-order descent methods for convex functions},
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year={2017},
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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},
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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{arora2018compressed,
title={A compressed sensing view of unsupervised text embeddings, bag-of-n-grams, and LSTMs},
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year={2018}
}
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year={2012},
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@article{yang2015sdpnal,
title={SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints},
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volume={7},
number={3},
pages={331--366},
year={2015},
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}
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title={The BFGS method with exact line searches fails for non-convex objective functions},
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year={2004},
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@inproceedings{boumal2016non,
title={The non-convex Burer-Monteiro approach works on smooth semidefinite programs},
author={Boumal, Nicolas and Voroninski, Vlad and Bandeira, Afonso},
booktitle={Advances in Neural Information Processing Systems},
pages={2757--2765},
year={2016}
}
@inproceedings{bhojanapalli2016dropping,
title={Dropping convexity for faster semi-definite optimization},
author={Bhojanapalli, Srinadh and Kyrillidis, Anastasios and Sanghavi, Sujay},
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pages={530--582},
year={2016}
}
@inproceedings{nesterov1983method,
title={A method for solving the convex programming problem with convergence rate O (1/k\^{} 2)},
author={Nesterov, Yurii E},
booktitle={Dokl. Akad. Nauk SSSR},
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pages={543--547},
year={1983}
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year={2017}
}
@article{fernandez2012local,
title={Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition},
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volume={22},
number={2},
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year={2012},
publisher={SIAM}
}
@article{bolte2018nonconvex,
title={Nonconvex Lagrangian-based optimization: monitoring schemes and global convergence},
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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},
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year={2018},
publisher={Elsevier}
}
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@inproceedings{yurtsever2015universal,
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}
@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,
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}
@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{hestenes1969multiplier,
title={Multiplier and gradient methods},
author={Hestenes, Magnus R},
journal={Journal of optimization theory and applications},
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pages={303--320},
year={1969},
publisher={Springer}
}
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title={A method for nonlinear constraints in minimization problems},
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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},
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year={2007}
}
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title={Iteration complexity of inexact augmented Lagrangian methods for constrained convex programming},
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year={2017}
}
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title={Computational complexity of inexact gradient augmented Lagrangian methods: application to constrained MPC},
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}
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Year = {2014}}
@article{boumal2016global,
Author = {Boumal, Nicolas and Absil, P-A and Cartis, Coralia},
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Year = {2016}}
@inproceedings{ge2016efficient,
Author = {Ge, Rong and Jin, Chi and Netrapalli, Praneeth and Sidford, Aaron and others},
Booktitle = {International Conference on Machine Learning},
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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,
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@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}}
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Author = {Park, Dohyung and Kyrillidis, Anastasios and Bhojanapalli, Srinadh and Caramanis, Constantine and Sanghavi, Sujay},
Journal = {arXiv preprint arXiv:1606.01316},
Title = {Provable Burer-Monteiro factorization for a class of norm-constrained matrix problems},
Year = {2016}}
@article{mixon2016clustering,
Author = {Mixon, Dustin G and Villar, Soledad and Ward, Rachel},
Journal = {arXiv preprint arXiv:1602.06612},
Title = {Clustering subgaussian mixtures by semidefinite programming},
Year = {2016}}
@article{yurtsever2018conditional,
Author = {Yurtsever, Alp and Fercoq, Olivier and Locatello, Francesco and Cevher, Volkan},
Journal = {arXiv preprint arXiv:1804.08544},
Title = {A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming},
Year = {2018}}
@inproceedings{jin2017escape,
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title={Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models},
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journal={SIAM Journal on Optimization},
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pages={951--967},
year={2016},
publisher={SIAM}
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@book{bertsekas2014constrained,
title={Constrained optimization and Lagrange multiplier methods},
author={Bertsekas, Dimitri P},
year={2014},
publisher={Academic press}
}
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Year = {2016}}
@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},
number={5},
pages={3109--3134},
year={2014},
publisher={SIAM}
}
@book{bertsekas1999nonlinear,
title={Nonlinear programming},
author={Bertsekas, Dimitri P}
}
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title={Multiplier and gradient methods},
author={Hestenes, Magnus R},
journal={Journal of optimization theory and applications},
volume={4},
number={5},
pages={303--320},
year={1969},
publisher={Springer}
}
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@article{park2016provable,
title={Provable Burer-Monteiro factorization for a class of norm-constrained matrix problems},
author={Park, Dohyung and Kyrillidis, Anastasios and Bhojanapalli, Srinadh and Caramanis, Constantine and Sanghavi, Sujay},
journal={arXiv preprint arXiv:1606.01316},
year={2016}
}
@article{mixon2016clustering,
title={Clustering subgaussian mixtures by semidefinite programming},
author={Mixon, Dustin G and Villar, Soledad and Ward, Rachel},
journal={arXiv preprint arXiv:1602.06612},
year={2016}
}
@inproceedings{kulis2007fast,
title={Fast low-rank semidefinite programming for embedding and clustering},
author={Kulis, Brian and Surendran, Arun C and Platt, John C},
booktitle={Artificial Intelligence and Statistics},
pages={235--242},
year={2007}
}
@article{Peng2007,
Author = {Peng, J. and Wei, Y.},
Date-Added = {2017-10-26 15:22:37 +0000},
Date-Modified = {2017-10-26 15:30:53 +0000},
Journal = {SIAM J. Optim.},
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