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