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% Created by Mehmet Fatih Sahin for nonconvex inexact augmented lagrangian paper
% December 14, Friday. 01:52 am

@article{ghadimi2016accelerated,
  title={Accelerated gradient methods for nonconvex nonlinear and stochastic programming},
  author={Ghadimi, Saeed and Lan, Guanghui},
  journal={Mathematical Programming},
  volume={156},
  number={1-2},
  pages={59--99},
  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{ge2016efficient,
	Author = {Ge, Rong and Jin, Chi and Netrapalli, Praneeth and Sidford, Aaron and others},
	Booktitle = {International Conference on Machine Learning},
	Pages = {2741--2750},
	Title = {Efficient algorithms for large-scale generalized eigenvector computation and canonical correlation analysis},
	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},
	Journal = {ACM Transactions on Mathematical Software (TOMS)},
	Number = {1},
	Pages = {1},
	Publisher = {ACM},
	Title = {The University of Florida sparse matrix collection},
	Volume = {38},
	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},
	Journal = {Journal of mathematical imaging and vision},
	Number = {1},
	Pages = {120--145},
	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}}

@article{park2016provable,
	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,
	Author = {Jin, Chi and Ge, Rong and Netrapalli, Praneeth and Kakade, Sham M and Jordan, Michael I},
	Booktitle = {International Conference on Machine Learning},
	Pages = {1724--1732},
	Title = {How to Escape Saddle Points Efficiently},
	Year = {2017}}

@article{doi:10.1137/15M1031631,
	Author = {Birgin, E. and Gardenghi, J. and Mart{\'\i}nez, J. and Santos, S. and Toint, P.},
	Doi = {10.1137/15M1031631},
	Eprint = {https://doi.org/10.1137/15M1031631},
	Journal = {SIAM Journal on Optimization},
	Number = {2},
	Pages = {951-967},
	Title = {Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models},
	Url = {https://doi.org/10.1137/15M1031631},
	Volume = {26},
	Year = {2016},
	Bdsk-Url-1 = {https://doi.org/10.1137/15M1031631},
	Bdsk-Url-2 = {http://dx.doi.org/10.1137/15M1031631}}
	
@article{liu2017linearized,
	Author = {Liu, Qinghua and Shen, Xinyue and Gu, Yuantao},
	Journal = {arXiv preprint arXiv:1705.02502},
	Title = {Linearized admm for non-convex non-smooth optimization with convergence analysis},
	Year = {2017}}
@article{wang2015global,
	Author = {Wang, Yu and Yin, Wotao and Zeng, Jinshan},
	Journal = {arXiv preprint arXiv:1511.06324},
	Title = {Global convergence of ADMM in nonconvex nonsmooth optimization},
	Year = {2015}}
	
@book{bertsekas2014constrained,
  title={Constrained optimization and Lagrange multiplier methods},
  author={Bertsekas, Dimitri P},
  year={2014},
  publisher={Academic press}
}
@article{lan2016iteration,
	Author = {Lan, Guanghui and Monteiro, Renato DC},
	Journal = {Mathematical Programming},
	Number = {1-2},
	Pages = {511--547},
	Publisher = {Springer},
	Title = {Iteration-complexity of first-order augmented Lagrangian methods for convex programming},
	Volume = {155},
	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}
}

@article{hestenes1969multiplier,
  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}
}

@incollection{powell1978fast,
  title={A fast algorithm for nonlinearly constrained optimization calculations},
  author={Powell, Michael JD},
  booktitle={Numerical analysis},
  pages={144--157},
  year={1978},
  publisher={Springer}
}

@article{burer2005local,
  title={Local minima and convergence in low-rank semidefinite programming},
  author={Burer, Samuel and Monteiro, Renato DC},
  journal={Mathematical Programming},
  volume={103},
  number={3},
  pages={427--444},
  year={2005},
  publisher={Springer}
}

@article{burer2003nonlinear,
  title={A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization},
  author={Burer, Samuel and Monteiro, Renato DC},
  journal={Mathematical Programming},
  volume={95},
  number={2},
  pages={329--357},
  year={2003},
  publisher={Springer}
}

@article{singer2011angular,
  title={Angular synchronization by eigenvectors and semidefinite programming},
  author={Singer, Amit},
  journal={Applied and computational harmonic analysis},
  volume={30},
  number={1},
  pages={20},
  year={2011},
  publisher={NIH Public Access}
}
@article{singer2011three,
  title={Three-dimensional structure determination from common lines in cryo-EM by eigenvectors and semidefinite programming},
  author={Singer, Amit and Shkolnisky, Yoel},
  journal={SIAM journal on imaging sciences},
  volume={4},
  number={2},
  pages={543--572},
  year={2011},
  publisher={SIAM}
}

@inproceedings{song2007dependence,
  title={A dependence maximization view of clustering},
  author={Song, Le and Smola, Alex and Gretton, Arthur and Borgwardt, Karsten M},
  booktitle={Proceedings of the 24th international conference on Machine learning},
  pages={815--822},
  year={2007},
  organization={ACM}
}

@inproceedings{mossel2015consistency,
  title={Consistency thresholds for the planted bisection model},
  author={Mossel, Elchanan and Neeman, Joe and Sly, Allan},
  booktitle={Proceedings of the forty-seventh annual ACM symposium on Theory of computing},
  pages={69--75},
  year={2015},
  organization={ACM}
}

@incollection{lovasz2003semidefinite,
  title={Semidefinite programs and combinatorial optimization},
  author={Lov{\'a}sz, L{\'a}szl{\'o}},
  booktitle={Recent advances in algorithms and combinatorics},
  pages={137--194},
  year={2003},
  publisher={Springer}
}

@article{khot2011grothendieck,
  title={Grothendieck-type inequalities in combinatorial optimization},
  author={Khot, Subhash and Naor, Assaf},
  journal={arXiv preprint arXiv:1108.2464},
  year={2011}
}

@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}
}