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@conference{alp2017aistats,
Address = {Fort Lauderdale},
Author = {Alp Yurtsever and Madeleine Udell and Joel Aaron Tropp and Volkan Cevher},
Booktitle = {20th International Conference on Artificial Intelligence and Statistics (AISTATS2017)},
Date-Added = {2017-10-02 12:53:44 +0000},
Date-Modified = {2017-10-02 12:53:44 +0000},
Title = {Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage},
Year = {2017}}
@inproceedings{JOELNIPS,
Author = {Tropp, Joel A and Yurtsever, Alp and Udell, Madeleine and Cevher, Volkan},
Booktitle = {Conference on Neural Information Processing Systems (NIPS)},
Note = {https://arxiv.org/abs/1706.05736},
Title = {Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data},
Year = {2017}}
@article{nesterov2005smooth,
Author = {Nesterov, Yu},
Journal = {Mathematical programming},
Number = {1},
Pages = {127--152},
Publisher = {Springer},
Title = {Smooth minimization of non-smooth functions},
Volume = {103},
Year = {2005}}
@article{calinescu2011maximizing,
Author = {Calinescu, Gruia and Chekuri, Chandra and P{\'a}l, Martin and Vondr{\'a}k, Jan},
Journal = {SIAM Journal on Computing},
Number = {6},
Pages = {1740--1766},
Publisher = {SIAM},
Title = {Maximizing a monotone submodular function subject to a matroid constraint},
Volume = {40},
Year = {2011}}
@article{chandrasekaran2012convex,
Author = {Chandrasekaran, Venkat and Recht, Benjamin and Parrilo, Pablo A and Willsky, Alan S},
Journal = {Foundations of Computational mathematics},
Number = {6},
Pages = {805--849},
Publisher = {Springer},
Title = {The convex geometry of linear inverse problems},
Volume = {12},
Year = {2012}}
@article{Bolte2014,
Abstract = {We introduce a proximal alternating linearized minimization (PALM) algorithm for solving a broad class of nonconvex and nonsmooth minimization problems. Building on the powerful Kurdyka--{\L}ojasiewicz property, we derive a self-contained convergence analysis framework and establish that each bounded sequence generated by PALM globally converges to a critical point. Our approach allows to analyze various classes of nonconvex-nonsmooth problems and related nonconvex proximal forward--backward algorithms with semi-algebraic problem's data, the later property being shared by many functions arising in a wide variety of fundamental applications. A by-product of our framework also shows that our results are new even in the convex setting. As an illustration of the results, we derive a new and simple globally convergent algorithm for solving the sparse nonnegative matrix factorization problem.},
Author = {Bolte, J{\'e}r{\^o}me and Sabach, Shoham and Teboulle, Marc},
Day = {01},
Doi = {10.1007/s10107-013-0701-9},
Issn = {1436-4646},
Journal = {Mathematical Programming},
Month = {Aug},
Number = {1},
Pages = {459--494},
Title = {Proximal alternating linearized minimization for nonconvex and nonsmooth problems},
Url = {https://doi.org/10.1007/s10107-013-0701-9},
Volume = {146},
Year = {2014},
Bdsk-Url-1 = {https://doi.org/10.1007/s10107-013-0701-9},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/s10107-013-0701-9}}
@conference{ilija2017colt,
Address = {Amsterdam},
Author = {Jonathan Scarlett and Ilija Bogunovic and Volkan Cevher},
Booktitle = {Conference on Learning Theory (COLT)},
Date-Added = {2017-10-02 07:53:06 +0000},
Date-Modified = {2017-10-02 07:53:46 +0000},
Title = {Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization},
Year = {2017}}
@conference{ilija2016nips,
Address = {Barcelona},
Author = {Ilija Bogunovic and Jonathan Scarlett and Andreas Krause and Volkan Cevher},
Booktitle = {Conference on Neural Information Processing Systems (NIPS)},
Date-Added = {2017-10-02 07:50:19 +0000},
Date-Modified = {2017-10-02 07:51:20 +0000},
Title = {Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation},
Year = {2016}}
@conference{ilija2016aistats,
Address = {Cadiz},
Author = {Ilija Bogunovic and Jonathan Scarlett and Volkan Cevher},
Booktitle = {International Conference on Artificial Intelligence and Statistics (AISTATS)},
Date-Added = {2017-10-02 07:43:14 +0000},
Date-Modified = {2017-10-02 07:49:46 +0000},
Title = {Time-Varying Gaussian Process Bandit Optimization},
Year = {2016}}
@article{Nesterov2009pdsubgradient,
Author = {Yurii Nesterov},
Date-Added = {2017-09-30 18:44:59 +0000},
Date-Modified = {2017-09-30 18:46:26 +0000},
Journal = {Mathematical Programming},
Number = {1, Ser. B},
Pages = {221-256},
Title = {Primal-Dual Subgradient Methods for Convex Problems},
Volume = {120},
Year = {2009}}
@article{Nesterov2007dualext,
Author = {Yurii Nesterov},
Date-Added = {2017-09-30 18:41:05 +0000},
Date-Modified = {2017-09-30 18:44:32 +0000},
Journal = {Mathematical Programming},
Number = {2-3},
Pages = {319--344},
Title = {Dual Extrapolation and its Applications to Solving Variational Inequalities and related Problems},
Volume = {109},
Year = {2007}}
@article{Duchi2011adagrad,
Author = {John Duchi and Elad Hazan and Yoram Singer},
Date-Added = {2017-09-30 18:34:15 +0000},
Date-Modified = {2017-09-30 18:36:47 +0000},
Journal = {Journal of Machine Learning Research},
Pages = {2121--2159},
Title = {Adaptive Subgradient Methods for Online Learning and Stochastic Optimization},
Volume = {12},
Year = {2011}}
@unpublished{Quoc2017asgard,
Author = {Quoc Tran-Dinh and Olivier Fercoq and Volkan Cevher},
Date-Added = {2017-09-30 18:02:29 +0000},
Date-Modified = {2017-10-01 08:58:55 +0000},
Note = {to appear in SIAM Journal on Optimization (SIOPT)},
Title = {A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization},
Year = {2017}}
@article{Zhao1998qap,
Author = {Qing Zhao and Stefan E. Karisch and Franz Rendl and Henry Wolkowicz},
Date-Added = {2017-09-26 13:52:54 +0000},
Date-Modified = {2017-09-26 13:54:01 +0000},
Journal = {Journal of Combinatorial Optimization},
Number = {1},
Pages = {71--109},
Title = {Semidefinite programming relaxations for the quadratic assignment problem},
Volume = {2},
Year = {1998}}
@article{Loiola2007,
Author = {Eliane Maria Loiola and Nair Maria Maia de Abreu and Paulo Oswaldo Boaventura-Netto and Peter Hahn and Tania Querido},
Date-Added = {2017-09-26 13:47:39 +0000},
Date-Modified = {2017-09-26 13:48:29 +0000},
Journal = {European Journal of Operational Research},
Number = {2},
Pages = {657--690},
Title = {A survey for the quadratic assignment problem},
Volume = {176},
Year = {2007}}
@article{Koopmans1957,
Author = {T. C. Koopmans, M. J. Beckmann},
Date-Added = {2017-09-26 13:45:05 +0000},
Date-Modified = {2017-09-26 13:46:05 +0000},
Journal = {Econometrica},
Pages = {53--76},
Title = {Assignment problems and the location of economic activities},
Volume = {25},
Year = {1957}}
@article{nemirovskii1983problem,
Author = {Nemirovskii, Arkadii and Yudin, David Borisovich and Dawson, Edgar Ronald},
Publisher = {Wiley},
Title = {Problem complexity and method efficiency in optimization},
Year = {1983}}
@article{ben2001ordered,
Author = {Ben-Tal, Aharon and Margalit, Tamar and Nemirovski, Arkadi},
Journal = {SIAM Journal on Optimization},
Number = {1},
Pages = {79--108},
Publisher = {SIAM},
Title = {The ordered subsets mirror descent optimization method with applications to tomography},
Volume = {12},
Year = {2001}}
@article{beck2003mirror,
Author = {Beck, Amir and Teboulle, Marc},
Journal = {Operations Research Letters},
Number = {3},
Pages = {167--175},
Publisher = {Elsevier},
Title = {Mirror descent and nonlinear projected subgradient methods for convex optimization},
Volume = {31},
Year = {2003}}
@article{Madani2014,
Author = {R. Madani, S. Sojoudi, J. Lavaei},
Date-Added = {2017-09-25 23:39:49 +0000},
Date-Modified = {2017-09-25 23:40:22 +0000},
Journal = {IEEE Transactions on Power Systems},
Title = {Convex relaxation for optimal power flow problem: mesh networks},
Year = {2014}}
@article{Sojoudi2012,
Author = {S. Sojoudi, J. Lavaei},
Date-Added = {2017-09-25 23:37:51 +0000},
Date-Modified = {2017-09-25 23:39:26 +0000},
Journal = {Proc. IEEE Power and Energy Soc. General Meeting},
Title = {Physics of power networks makes hard optimization problems easy to solve},
Year = {2012}}
@article{Zhang2011,
Author = {B. Zhang, D. Tse},
Date-Added = {2017-09-25 23:37:05 +0000},
Date-Modified = {2017-09-25 23:37:47 +0000},
Journal = {Proc. 49th Annu. Allerton Conf.},
Title = {Geometry of feasible injection region of power networks},
Year = {2011}}
@article{Lavaei2012,
Author = {J. Lavaei, S. Low},
Date-Added = {2017-09-25 23:34:24 +0000},
Date-Modified = {2017-09-25 23:35:20 +0000},
Journal = {IEEE Transactions on Power Systems},
Title = {Zero duality gap in optimal power flow problem},
Year = {2012}}
@inproceedings{alpnips,
Author = {Yurtsever, Alp and Dinh, Quoc Tran and Cevher, Volkan},
Booktitle = {Advances in Neural Information Processing Systems},
Pages = {3150--3158},
Title = {A universal primal-dual convex optimization framework},
Year = {2015}}
@inproceedings{becker2013randomized,
Address = {Bremen},
Author = {Stephen Becker and Volkan Cevher and Anastasios Kyrillidis},
Booktitle = {10th International Conference on Sampling Theory and Applications (Sampta)},
Date-Added = {2016-10-02 16:18:29 +0000},
Date-Modified = {2016-10-02 16:19:46 +0000},
Title = {Randomized Low-Memory Singular Value Projection},
Year = {2013}}
@inproceedings{nips,
Address = {Montr{\'e}al},
Author = {Carlson David and Edo Collins and Ya-Ping Hsieh and Lawrance Carin and Volkan Cevher},
Booktitle = {Proc. 29th Ann. Conf. Neural Information Processings (NIPS)},
Date-Added = {2016-10-02 16:15:06 +0000},
Date-Modified = {2016-10-02 16:16:43 +0000},
Title = {Preconditioned Spectral Descent for Deep Learning},
Year = {2015}}
@inproceedings{tasosALPS,
Author = {A. Kyrillidis and V. Cevher},
Booktitle = {IEEE Statistical Signal Processing Workshop (SSP)},
Date-Added = {2016-10-02 16:10:49 +0000},
Date-Modified = {2016-10-02 16:11:43 +0000},
Pages = {185--188},
Title = {MATRIX ALPS: Accelerated low rank and sparse matrix reconstruction},
Year = {2012}}
@article{JOELSIMAX,
Author = {Joel Aaron Tropp and Alp Yurtsever and Madeleine Udell and Volkan Cevher},
Date-Added = {2016-10-02 15:54:03 +0000},
Date-Modified = {2016-10-02 16:08:35 +0000},
Journal = {SIAM Journal on Matrix Analysis and Applications (SIMAX)},
Note = {https://arxiv.org/abs/1609.00048},
Title = {Randomized single-view algorithms for low-rank matrix approximation},
Year = {2016}}
@unpublished{bang2016,
Author = {Cevher, Volkan and Vu, Cong Bang and Yurtsever, Alp},
Date-Added = {2016-10-02 15:49:48 +0000},
Date-Modified = {2016-10-02 15:52:48 +0000},
Title = {Stochastic Forward-{D}ouglas-{R}achford Splitting for Monotone Inclusions},
Year = {2016}}
@article{cevher2014convex,
Author = {Cevher, Volkan and Becker, Steffen and Schmidt, Martin},
Date-Added = {2016-10-02 15:48:07 +0000},
Date-Modified = {2016-10-02 15:48:52 +0000},
Journal = {Signal Processing Magazine, IEEE},
Number = {5},
Pages = {32--43},
Title = {Convex optimization for big data: Scalable, randomized, and parallel algorithms for big data analytics},
Volume = {31},
Year = {2014}}
@conference{TranDinh2014b,
Address = {Montreal, Canada},
Author = {Q. Tran-Dinh and V. Cevher},
Booktitle = {Proc. the Neural Information Processing Systems Foundation conference (NIPS2014)},
Date-Added = {2016-10-02 15:45:01 +0000},
Date-Modified = {2016-10-02 15:45:01 +0000},
Month = {December},
Owner = {quoctd},
Pages = {1--9},
Timestamp = {2014.09.25},
Title = {Constrained convex minimization via model-based excessive gap},
Year = {2014}}
@article{Juditsky2013a,
Author = {A. Juditsky and A. Nemirovski},
Date-Added = {2016-10-02 15:25:46 +0000},
Date-Modified = {2016-10-02 15:25:46 +0000},
Journal = {Tech. Report.},
Owner = {quoctd},
Timestamp = {2015.02.07},
Title = {Solving variational inequalities with monotone operators on domains given by linear minimization oracles},
Volume = {http://arxiv.org/abs/1312.1073},
Year = {2013}}
@article{https://arxiv.org/abs/1603.01681,
Author = {Quoc Tran-Dinh and Anastasios Kyrillidis and Volkan Cevher},
Date-Added = {2016-10-02 15:21:38 +0000},
Date-Modified = {2016-10-02 15:23:52 +0000},
Journal = {Mathematics of {O}perations {R}esearch},
Note = {http://arxiv.org/abs/1603.01681},
Publisher = {INFORMS},
Title = {A single-phase, proximal path-following framework},
Year = {2016}}
@article{tran2015compositeJMLR,
Author = {Quoc Tran-Dinh and Anastasios Kyrillidis and Volkan Cevher},
Date-Added = {2016-10-02 15:14:56 +0000},
Date-Modified = {2016-10-02 15:17:36 +0000},
Journal = {Journal of Machine Learning Research},
Pages = {371--416},
Title = {Composite Self-Concordant Minimization},
Volume = {16},
Year = {2015}}
@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{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}
}
@article{hestenes1969multiplier,
title={Multiplier and gradient methods},
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@book{bertsekas2014constrained,
title={Constrained optimization and Lagrange multiplier methods},
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title={On the linear convergence of the alternating direction method of multipliers},
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volume={162},
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year={2017},
publisher={Springer}
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title={On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues},
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title={Nonlinear programming},
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year={1999},
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@article{lan2016iteration,
title={Iteration-complexity of first-order augmented Lagrangian methods for convex programming},
author={Lan, Guanghui and Monteiro, Renato DC},
journal={Mathematical Programming},
volume={155},
number={1-2},
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year={2016},
publisher={Springer}
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@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},
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publisher={SIAM}
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title={Global convergence of ADMM in nonconvex nonsmooth optimization},
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year={2015}
}
@article{liu2017linearized,
title={Linearized admm for non-convex non-smooth optimization with convergence analysis},
author={Liu, Qinghua and Shen, Xinyue and Gu, Yuantao},
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year={2017}
}
@article{boumal2014manopt,
title={Manopt, a Matlab toolbox for optimization on manifolds},
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@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}
}
@inproceedings{ge2016efficient,
title={Efficient algorithms for large-scale generalized eigenvector computation and canonical correlation analysis},
author={Ge, Rong and Jin, Chi and Netrapalli, Praneeth and Sidford, Aaron and others},
booktitle={International Conference on Machine Learning},
pages={2741--2750},
year={2016}
}
@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}
}
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author={Clason, Christian and Mazurenko, Stanislav and Valkonen, Tuomo},
journal={arXiv preprint arXiv:1802.03347},
year={2018}
}
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title={A first-order primal-dual algorithm for convex problems with applications to imaging},
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year={2011},
publisher={Springer}
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@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}
}
@article{bhojanapalli2018smoothed,
title={Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form},
author={Bhojanapalli, Srinadh and Boumal, Nicolas and Jain, Prateek and Netrapalli, Praneeth},
journal={arXiv preprint arXiv:1803.00186},
year={2018}
}
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title={Provable Burer-Monteiro factorization for a class of norm-constrained matrix problems},
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journal={arXiv preprint arXiv:1606.01316},
year={2016}
}
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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}
}
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journal={Mathematical Programming},
volume={155},
number={1-2},
pages={267--305},
year={2016},
publisher={Springer}
}
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