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@book{livre1,
title={Convex analysis and monotone operator theory in Hilbert spaces},
author={Bauschke, Heinz H and Combettes, Patrick L},
volume={408},
year={2011},
publisher={Springer}
}
@article{Nes05,
title={Smooth minimization of non-smooth functions},
author={Nesterov, Yu},
journal={Math. Program.},
volume={103},
number={1},
pages={127--152},
year={2005},
publisher={SIAM}
}
@Article{Chambolle2011,
author="Chambolle, Antonin
and Pock, Thomas",
title="A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging",
journal="Journal of Mathematical Imaging and Vision",
year="2011",
month="May",
day="01",
volume="40",
number="1",
pages="120--145"
}
@Article{Combettes2012,
author="Combettes, Patrick L.
and Pesquet, Jean-Christophe",
title="Primal-Dual Splitting Algorithm for Solving Inclusions with Mixtures of Composite, Lipschitzian, and Parallel-Sum Type Monotone Operators",
journal="Set-Valued and Variational Analysis",
year="2012",
month="Jun",
day="01",
volume="20",
number="2",
pages="307--330"
}
@Article{Burer2005,
author="Burer, Samuel
and Monteiro, Renato D.C.",
title="Local Minima and Convergence in Low-Rank Semidefinite Programming",
journal="Mathematical Programming",
year="2005",
month="Jul",
day="01",
volume="103",
number="3",
pages="427--444"
}
@Article{Burer2003,
author="Burer, Samuel
and Monteiro, Renato D.C.",
title="A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization",
journal="Mathematical Programming",
year="2003",
month="Feb",
day="01",
volume="95",
number="2",
pages="329--357"
}
@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}
}
@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{chen2015fast,
title={Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees},
author={Chen, Yudong and Wainwright, Martin J},
journal={arXiv preprint arXiv:1509.03025},
year={2015}
}
@inproceedings{zhao2015nonconvex,
title={A nonconvex optimization framework for low rank matrix estimation},
author={Zhao, Tuo and Wang, Zhaoran and Liu, Han},
booktitle={Advances in Neural Information Processing Systems},
pages={559--567},
year={2015}
}
@inproceedings{jain2010guaranteed,
title={Guaranteed rank minimization via singular value projection},
author={Jain, Prateek and Meka, Raghu and Dhillon, Inderjit S},
booktitle={Advances in Neural Information Processing Systems},
pages={937--945},
year={2010}
}
@article{becker2013randomized,
title={Randomized low-memory singular value projection},
author={Becker, Stephen and Cevher, Volkan and Kyrillidis, Anastasios},
journal={arXiv preprint arXiv:1303.0167},
year={2013}
}
@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{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}
}
@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}
}
@article{boumal2016global,
title={Global rates of convergence for nonconvex optimization on manifolds},
author={Boumal, Nicolas and Absil, P-A and Cartis, Coralia},
journal={arXiv preprint arXiv:1605.08101},
year={2016}
}
@article{Lan16,
title={Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization},
author={S. Ghadimi,G. Lan, H. Xhang},
journal={ Math. Program., Ser. A},
volume = {155},
pages = {267--305},
year={2016}
}
@Article{Hare2009,
title={Computing proximal points of nonconvex functions},
author={Hare, Warren and Sagastiz{\'a}bal, Claudia},
journal={Mathematical Programming},
year={2009},
volume={116},
number={1},
pages={221--258}
}
@book{arrow2012studies,
title={Studies in Linear and Non-Linear Programming: Stanford Mathematical Studies in the Social Sciences},
author={Arrow, K.J. and Hurwicz, L. and Uzawa, H.},
number={no. 2},
isbn={9781258450144},
url={https://books.google.ch/books?id=cuJnMQEACAAJ},
year={2012},
publisher={Literary Licensing, LLC}
}
@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,
title={Mini-Batch Stochastic ADMMs for Nonconvex Nonsmooth Optimization},
author={Huang, Feihu and Chen, Songcan},
journal={arXiv preprint arXiv:1802.03284},
year={2018}
}
@article{Valkonen14,
author={Tuomo Valkonen},
title={A primal-dual hybrid gradient method for nonlinear operators with applications to MRI},
journal={Inverse Problems},
volume={30},
number={5},
pages={055012},
url={http://stacks.iop.org/0266-5611/30/i=5/a=055012},
year={2014}
}
@inproceedings{zhou2010stable,
title={Stable principal component pursuit},
author={Zhou, Zihan and Li, Xiaodong and Wright, John and Candes, Emmanuel and Ma, Yi},
booktitle={Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on},
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"
}
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