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@Article{Chambolle2011,
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}
@Article{Combettes2012,
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@Article{Burer2003,
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@article{park2016provable,
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  year={2016}
}
@inproceedings{bhojanapalli2016dropping,
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  pages={530--582},
  year={2016}
}
@article{chen2015fast,
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@inproceedings{zhao2015nonconvex,
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@inproceedings{jain2010guaranteed,
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@article{becker2013randomized,
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@inproceedings{yurtsever2015universal,
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  year={2015}
}
@article{tran2018smooth,
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  volume={28},
  number={1},
  pages={96--134},
  year={2018},
  publisher={SIAM}
}
@inproceedings{boumal2016non,
  title={The non-convex Burer-Monteiro approach works on smooth semidefinite programs},
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  year={2016}
}
@article{boumal2016global,
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  year={2016}
}
@article{Lan16,
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	volume = {155},
	pages = {267--305},
	year={2016}
}
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@book{arrow2012studies,
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	year={2012},
	publisher={Literary Licensing, LLC}
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@article{chambolle_pock_2016, title={An introduction to continuous optimization for imaging}, volume={25}, DOI={10.1017/S096249291600009X}, journal={Acta Numerica}, publisher={Cambridge University Press}, author={Chambolle, Antonin and Pock, Thomas}, year={2016}, pages={161--319}
}
@article{huang2018mini,
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	author={Huang, Feihu and Chen, Songcan},
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	year={2018}
}
	
	@article{Valkonen14,
		author={Tuomo Valkonen},
		title={A primal-dual hybrid gradient method for nonlinear operators with applications to MRI},
		journal={Inverse Problems},
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		number={5},
		pages={055012},
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		year={2014}
	}
@inproceedings{zhou2010stable,
	title={Stable principal component pursuit},
	author={Zhou, Zihan and Li, Xiaodong and Wright, John and Candes, Emmanuel and Ma, Yi},
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	pages={1518--1522},
	year={2010},
	organization={IEEE}
}
@article{jain2017non,
	title={Non-convex optimization for machine learning},
	author={Jain, Prateek and Kar, Purushottam},
	journal={Foundations and Trends{\textregistered} in Machine Learning},
	volume={10},
	number={3-4},
	pages={142--336},
	year={2017},
	publisher={Now Publishers, Inc.}
}
@article{komodakis2015playing,
	title={Playing with duality: An overview of recent primal? dual approaches for solving large-scale optimization problems},
	author={Komodakis, Nikos and Pesquet, Jean-Christophe},
	journal={IEEE Signal Processing Magazine},
	volume={32},
	number={6},
	pages={31--54},
	year={2015},
	publisher={IEEE}
}


@article{mollenhoff2015primal,
	title={The primal-dual hybrid gradient method for semiconvex splittings},
	author={Mollenhoff, Thomas and Strekalovskiy, Evgeny and Moeller, Michael and Cremers, Daniel},
	journal={SIAM Journal on Imaging Sciences},
	volume={8},
	number={2},
	pages={827--857},
	year={2015},
	publisher={SIAM}
}
@article{artina2013linearly,
	title={Linearly constrained nonsmooth and nonconvex minimization},
	author={Artina, Marco and Fornasier, Massimo and Solombrino, Francesco},
	journal={SIAM Journal on Optimization},
	volume={23},
	number={3},
	pages={1904--1937},
	year={2013},
	publisher={SIAM}
}
@InProceedings{Matin17,
	author="Benning, Martin
	and Knoll, Florian
	and Sch{\"o}nlieb, Carola-Bibiane
	and Valkonen, Tuomo",
	editor="Bociu, Lorena
	and D{\'e}sid{\'e}ri, Jean-Antoine
	and Habbal, Abderrahmane",
	title="Preconditioned ADMM with Nonlinear Operator Constraint",
	booktitle="System Modeling and Optimization",
	year="2016",
	publisher="Springer International Publishing",
	address="Cham",
	pages="117--126",
	abstract="We are presenting a modification of the well-known Alternating Direction Method of Multipliers (ADMM) algorithm with additional preconditioning that aims at solving convex optimisation problems with nonlinear operator constraints. Connections to the recently developed Nonlinear Primal-Dual Hybrid Gradient Method (NL-PDHGM) are presented, and the algorithm is demonstrated to handle the nonlinear inverse problem of parallel Magnetic Resonance Imaging (MRI).",
	isbn="978-3-319-55795-3"
}