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@article{Jester1996,
Author = {Hamilton-Jester, C. L. and Li, C.-K.},
Date-Added = {2018-02-08 21:07:43 +0000},
Date-Modified = {2018-02-08 21:09:35 +0000},
Journal = {Rocky Mountain J. Math.},
Number = {4},
Pages = {1371--1383},
Title = {Extreme vectors of doubly nonnegative matrices},
Volume = {26},
Year = {1996}}
@article{Liu2013,
Author = {Liu, J. and Musialski, P. and Wonka, P. and Ye, J.},
Date-Added = {2018-02-08 18:27:25 +0000},
Date-Modified = {2018-02-08 18:28:52 +0000},
Journal = {{IEEE} Trans. Pattern Anal. Mach. Intell},
Number = {1},
Pages = {208--230},
Title = {Tensor completion for estimating missing values in visual data},
Volume = {35},
Year = {2013}}
@article{Zeng2018,
Author = {Zeng, W.-J. and So, H. C.},
Date-Added = {2018-02-08 18:24:12 +0000},
Date-Modified = {2018-02-08 18:26:12 +0000},
Journal = {{IEEE} Trans. on Sig. Process},
Number = {5},
Pages = {1125--1140},
Title = {Outlier--Robust Matrix Completion via $\ell_p$-Minimization},
Volume = {66},
Year = {2018}}
@unpublished{Xu2017,
Author = {Xu, H.-K.},
Date-Added = {2018-02-07 09:45:36 +0000},
Date-Modified = {2018-02-07 09:46:20 +0000},
Note = {arXiv:1710.07367v1},
Title = {Convergence Analysis of the {F}rank--{W}olfe Algorithm and Its Generalization in {B}anach Spaces},
Year = {2017}}
@conference{Dunner2016,
Author = {D\"unner, C. and Forte, S. and Tak\'ac, M. and Jaggi, M.},
Booktitle = {Proc. $33$rd Int. Conf. Machine Learning},
Date-Added = {2018-02-07 01:03:32 +0000},
Date-Modified = {2018-02-07 01:04:42 +0000},
Title = {Primal--Dual Rates and Certificates},
Year = {2016}}
@unpublished{Lan2014,
Author = {G. Lan},
Date-Added = {2018-02-06 17:11:13 +0000},
Date-Modified = {2018-02-06 17:11:13 +0000},
Note = {arXiv:1309.5550v2},
Title = {The Complexity of Large--Scale Convex Programming under a Linear Optimization Oracle},
Year = {2014}}
@article{Yang2015,
Author = {Yang, L. and Sun, D. and Toh, K-.C.},
Date-Added = {2018-01-16 21:00:53 +0000},
Date-Modified = {2018-01-16 21:04:16 +0000},
Journal = {Mathematical Programming Computation},
Number = {3},
Pages = {331-366},
Title = {{SDPNAL}+: A majorized semismooth {N}ewton--{CG} augmented {L}agrangian method for semidefinite programming with nonnegative constraints},
Volume = {7},
Year = {2015}}
@webpage{MNIST,
Author = {LeCun, Y. and Cortes, C.},
Date-Added = {2018-01-16 20:36:46 +0000},
Date-Modified = {2018-01-16 20:44:36 +0000},
Month = {Accessed: Jan. 2016},
Title = {{MNIST} handwritten digit database},
Url = {http://yann.lecun.com/exdb/mnist/},
Bdsk-Url-1 = {http://yann.lecun.com/exdb/mnist/}}
@article{Mixon2017,
Author = {Mixon, D. G. and Villar, S. and Ward, R.},
Date-Added = {2018-01-16 20:34:35 +0000},
Date-Modified = {2018-01-16 20:35:59 +0000},
Journal = {Information and Inference: A Journal of the IMA},
Number = {4},
Pages = {389--415},
Title = {Clustering subgaussian mixtures by semidefinite programming},
Volume = {6},
Year = {2017}}
@book{VonNeumann1944,
Author = {Von Neumann, J. and Morgenstern, O.},
Date-Added = {2018-01-13 18:19:54 +0000},
Date-Modified = {2018-01-13 18:21:16 +0000},
Publisher = {Princeton press},
Title = {Theory of games and economic behavior},
Year = {1944}}
@article{Taskar2006,
Author = {Taskar, B. and Lacoste-Julien, S. and Jordan, M.I.},
Date-Added = {2018-01-13 18:17:27 +0000},
Date-Modified = {2018-01-13 18:18:54 +0000},
Journal = {Journal of Machine Learning Research},
Title = {Structured prediction, dual extragradient and {B}regman projections},
Year = {2006}}
@conference{richard2012estimation,
Author = {Richard, E. and Savalle, P.-A. and Vayatis, N.},
Booktitle = {Proceedings of the $29$th International Conference on Machine Learning},
Date-Modified = {2018-01-13 08:25:26 +0000},
Title = {Estimation of simultaneously sparse and low rank matrices},
Year = {2012}}
@conference{yen2016convex,
Author = {Yen, I. E.-H. and Lin, X. and Zhang, J. and Ravikumar, P. and Dhillon, I. S.},
Booktitle = {Proceedings of the $33$rd International Conference on Machine Learning},
Date-Modified = {2018-01-16 20:33:23 +0000},
Title = {A convex atomic--norm approach to multiple sequence alignment and motif discovery},
Year = {2016}}
@conference{JulienLacoste2015,
Author = {Lacoste-Julien, S. and Jaggi, M.},
Booktitle = {Advances in Neural Information Processing Systems 28},
Date-Added = {2018-01-01 05:03:16 +0000},
Date-Modified = {2018-01-01 05:13:35 +0000},
Title = {On the Global Linear Convergence of {F}rank-{W}olfe Optimization Variants},
Year = {2015}}
@article{Guelat1986,
Author = {Gu\'elat, J. and Marcotte, P.},
Date-Added = {2018-01-01 05:00:46 +0000},
Date-Modified = {2018-01-01 05:01:56 +0000},
Journal = {Math. Program.},
Number = {1},
Pages = {110--119},
Title = {Some Comments on {W}olfe's `Away Step'},
Volume = {35},
Year = {1986}}
@article{Beck2004,
Author = {Beck, A.},
Date-Added = {2018-01-01 04:58:40 +0000},
Date-Modified = {2018-01-01 04:59:53 +0000},
Journal = {Mathematical Methods of Operations Research},
Number = {2},
Pages = {235--247},
Title = {A Conditional Gradient Method with Linear Rate of Convergence for Solving Convex Linear Systems},
Volume = {59},
Year = {2004}}
@conference{Garber2015,
Author = {Garber, D. and Hazan, E.},
Booktitle = {Proceedings of the $32$nd International Conference on Machine Learning},
Date-Added = {2018-01-01 04:56:22 +0000},
Date-Modified = {2018-01-01 04:57:29 +0000},
Title = {Faster Rates for the {F}rank-{W}olfe Method over Strongly-Convex Sets},
Year = {2015}}
@conference{Alacaoglu2017,
Author = {Alacaoglu, A. and Tran--Dinh, Q. and Fercoq, O. and Cevher, V.},
Booktitle = {Advances in Neural Information Processing Systems 30},
Date-Added = {2017-12-30 16:03:02 +0000},
Date-Modified = {2017-12-30 16:04:19 +0000},
Title = {Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization},
Year = {2017}}
@article{Nesterov2005,
Author = {Nesterov, Y.},
Date-Added = {2017-12-30 12:02:55 +0000},
Date-Modified = {2017-12-30 12:04:01 +0000},
Journal = {Math. Program.},
Pages = {127--152},
Title = {Smooth Minimization of Non-smooth Functions},
Volume = {103},
Year = {2005}}
@conference{Odor2016,
Author = {Odor, G. and Li, Y.-H. and Yurtsever, A. and Hsieh, Y.-P. and Tran--Dinh, Q. and El~Halabi, M. and Cevher, V.},
Booktitle = {$41$st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
Date-Added = {2017-12-30 02:13:12 +0000},
Date-Modified = {2017-12-30 02:16:37 +0000},
Title = {{F}rank-{W}olfe Works for Non-Lipschitz Continuous Gradient Objectives: Scalable Poisson Phase Retrieval},
Year = {2016}}
@article{Nesterov2017,
Author = {Nesterov, Y.},
Date-Added = {2017-12-30 02:09:57 +0000},
Date-Modified = {2017-12-30 02:11:15 +0000},
Journal = {Math. Program.},
Title = {Complexity Bounds for Primal-Dual Methods Minimizing the Model of Objective Function},
Year = {2017}}
@conference{Gidel2017,
Author = {Gidel, G. and Jebara, T. and Lacoste-Julien, S.},
Booktitle = {Proceedings of the $20$th International Conference on Artificial Intelligence and Statistics (AISTATS)},
Date-Added = {2017-12-30 02:00:44 +0000},
Date-Modified = {2017-12-30 02:02:14 +0000},
Title = {{F}rank-{Wolfe} Algorithms for Saddle Point Problems},
Year = {2017}}
@conference{Hazan2008,
Author = {Hazan, E.},
Booktitle = {LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics},
Date-Added = {2017-12-30 00:44:16 +0000},
Date-Modified = {2017-12-30 00:45:27 +0000},
Pages = {306--316},
Title = {Sparse Approximate Solutions to Semidefinite Programs},
Year = {2008}}
@article{Clarkson2010,
Author = {Clarkson, K. L.},
Date-Added = {2017-12-30 00:41:25 +0000},
Date-Modified = {2017-12-30 00:42:16 +0000},
Journal = {ACM Transactions on Algorithms (TALG)},
Number = {4},
Title = {Coresets, Sparse Greedy Approximation, and the {F}rank-{W}olfe Algorithm},
Volume = {6},
Year = {2010}}
@article{Nesterov1983,
Author = {Nesterov, Y.},
Date-Added = {2017-12-30 00:34:10 +0000},
Date-Modified = {2017-12-30 00:35:19 +0000},
Journal = {Soviet Mathematics Doklady},
Number = {2},
Pages = {372--376},
Title = {A Method of Solving a Convex Programming Problem with Convergence Rate {$O( 1 / k^2 )$}},
Volume = {27},
Year = {1987}}
@conference{Hazan2016,
Author = {Hazan, E. and Luo, H.},
Booktitle = {Proceedings of the $33$rd International Conference on Machine Learning},
Date-Added = {2017-12-30 00:28:22 +0000},
Date-Modified = {2017-12-30 00:29:50 +0000},
Title = {Variance-Reduced and Projection-Free Stochastic Optimization},
Year = {2016}}
@article{Dunn1980,
Author = {Dunn, J.},
Date-Added = {2017-12-29 15:08:44 +0000},
Date-Modified = {2017-12-29 15:09:31 +0000},
Journal = {SIAM J. Control Optim.},
Number = {5},
Pages = {473--487},
Title = {Convergence Rates for Conditional Gradient Sequences Generated by Implicit Step Length Rules},
Volume = {18},
Year = {1980}}
@article{Dunn1979,
Author = {Dunn, J.},
Date-Added = {2017-12-29 15:06:12 +0000},
Date-Modified = {2017-12-29 15:07:48 +0000},
Journal = {SIAM J. Control Optim.},
Number = {2},
Pages = {187--211},
Title = {Rates of Convergence for Conditional Gradient Algorithms Near Singular and Nonsinglular Extremals},
Volume = {17},
Year = {1979}}
@article{Dunn1978,
Author = {Dunn, J. and Harshbarger, S.},
Date-Added = {2017-12-29 15:03:16 +0000},
Date-Modified = {2017-12-29 15:06:28 +0000},
Journal = {Journal of Mathematical Analysis and Applications},
Number = {2},
Pages = {432--444},
Title = {Conditional Gradient Algorithms with Open Loop Step Size Rules},
Volume = {62},
Year = {1978}}
@article{Levitin1966,
Author = {Levitin, E. and Polyak, B.},
Date-Added = {2017-12-29 15:01:05 +0000},
Date-Modified = {2017-12-29 15:02:00 +0000},
Journal = {USSR Computational Mathematics and Mathematical Physics},
Number = {5},
Pages = {1--50},
Title = {Constrained Minimization Methods},
Volume = {6},
Year = {1966}}
@article{FrankWolfe1956,
Author = {Frank, M. and Wolfe, P.},
Date-Added = {2017-12-29 14:31:07 +0000},
Date-Modified = {2017-12-29 14:33:45 +0000},
Journal = {Naval Research Logistics Quarterly},
Pages = {95--110},
Title = {An Algorithm for Quadratic Programming},
Volume = {3},
Year = {1956}}
@article{Zhao1998qap,
Author = {Qing Zhao and Stefan E. Karisch and Franz Rendl and Henry Wolkowicz},
Date-Added = {2017-11-03 22:18:29 +0000},
Date-Modified = {2017-11-03 22:18:29 +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 = {Loiola, E.M. and de Abreu, N.M.M. and Boaventura-Netto, P.O. and Hahn, P. and Querido, T.},
Date-Added = {2017-11-03 22:18:07 +0000},
Date-Modified = {2017-11-03 22:24:01 +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{Garber2016,
Author = {Garber, D. and Hazan, E.},
Date-Added = {2017-11-03 21:46:13 +0000},
Date-Modified = {2017-11-03 21:47:48 +0000},
Journal = {Mathematical Programming, Ser. A},
Number = {158},
Pages = {329--361},
Title = {Sublinear time algorithms for approximate semidefinite programming},
Year = {2016}}
@conference{Yoshise2010,
Address = {Yokohama},
Author = {Yoshise, A. and Matsukawa, Y.},
Booktitle = {{IEEE} {I}nternational Symposium on Computer-Aided Control System Design},
Date-Added = {2017-11-03 15:38:24 +0000},
Date-Modified = {2017-11-03 15:39:47 +0000},
Pages = {13--18},
Title = {On optimization over the doubly nonnegative cone},
Year = {2010}}
@inproceedings{Yurtsever2016,
Address = {Fort Lauderdale},
Author = {Yurtsever, A. and Udell, M. and Tropp, J.A. and Cevher, V.},
Booktitle = {Proc. 20th Int. Conf. Artificial Intelligence and Statistics (AISTATS)},
Date-Added = {2017-11-03 15:24:37 +0000},
Date-Modified = {2017-11-03 15:27:09 +0000},
Month = {May},
Title = {Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage},
Year = {2017}}
@article{Lavaei2012,
Author = {Lavaei, J. and Low, H.L.},
Date-Added = {2017-10-31 14:40:12 +0000},
Date-Modified = {2017-10-31 14:43:52 +0000},
Journal = {{IEEE} Trans. on Power Syst.},
Month = {February},
Number = {1},
Pages = {92--107},
Title = {Zero Duality Gap in Optimal Power Flow Problem},
Volume = {27},
Year = {2012}}
@article{Bandeira2016,
Author = {Bandeira, A.S. and Boumal, N. and Voroninski, V.},
Date-Added = {2017-10-26 15:53:31 +0000},
Date-Modified = {2017-10-26 15:54:35 +0000},
Journal = {{JMLR}: Workshop and Conference Proceedings},
Pages = {1--22},
Title = {On the low-rank approach for semidefinite programs arising in synchronization and community detection},
Volume = {49},
Year = {2016}}
@article{jaggi2011convex,
Author = {Jaggi, M.},
Date-Modified = {2017-10-31 15:01:25 +0000},
Journal = {arXiv preprint arXiv:1108.1170},
Title = {Convex optimization without projection steps},
Year = {2011}}
@inproceedings{lacoste2012block,
Address = {Atlanta, Georgia, USA},
Author = {Lacoste-Julien, S. and Jaggi, M. and Schmidt, M. and Pletscher, P.},
Booktitle = {Proc. $30$th Int. Conf. Machine Learning},
Date-Modified = {2017-11-06 23:36:35 +0000},
Journal = {arXiv preprint arXiv:1207.4747},
Title = {Block-coordinate Frank-Wolfe optimization for structural SVMs},
Year = {2013}}
@article{Ahmed2014,
Author = {Ahmed, A. and Recht, B. and Romberg, J.},
Date-Added = {2017-10-26 15:45:03 +0000},
Date-Modified = {2017-10-26 15:49:20 +0000},
Journal = {{IEEE} Trans. on Inf. Theory},
Number = {3},
Pages = {1711--1732},
Title = {Blind Deconvolution Using Convex Programming},
Volume = {60},
Year = {2014}}
@article{Lanckriet2004,
Author = {Lanckriet, G.R.G. and Cristianini, N. and Ghaoui, L.E. and Bartlett, P. and Jordan, M.I.},
Date-Added = {2017-10-26 15:38:58 +0000},
Date-Modified = {2017-10-26 15:41:29 +0000},
Journal = {Journal of Machine Learning Research},
Pages = {27--72},
Title = {Learning the kernel matrix with semidefinite programming},
Volume = {5},
Year = {2004}}
@article{dAspremont2004,
Author = {d'Aspremont, A. and Ghaoui, L.E. and Jordan, M.I. and Lanckriet, G.R.G.},
Date-Added = {2017-10-26 15:34:19 +0000},
Date-Modified = {2017-10-26 15:39:57 +0000},
Journal = {SIAM Review},
Number = {3},
Pages = {434--448},
Title = {A Direct Formulation for Sparse {PCA} Using Semidefinite Programming},
Volume = {49},
Year = {2007}}
@article{Peng2007,
Author = {Peng, J. and Wei, Y.},
Date-Added = {2017-10-26 15:22:37 +0000},
Date-Modified = {2017-10-26 15:30:53 +0000},
Journal = {SIAM J. Optim.},
Number = {1},
Pages = {186--205},
Title = {Approximating {K}--means--type clustering via semidefinite programming},
Volume = {18},
Year = {2007}}
@inproceedings{Hazan2012,
Author = {Hazan, E. and Kale, S.},
Booktitle = {Proceedings of the $29$th International Conference on Machine Learning},
Date-Added = {2017-10-26 14:40:57 +0000},
Date-Modified = {2017-10-26 14:42:00 +0000},
Title = {Projection--free Online Learning},
Year = {2012}}
@unpublished{TranDinh2017,
Author = {Tran--Dinh, Q. and Fercoq, O. and Cevher, V.},
Date-Added = {2017-10-26 14:38:40 +0000},
Date-Modified = {2017-12-30 16:06:44 +0000},
Note = {arXiv:1507.06243},
Title = {A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization},
Year = {2017}}
@inproceedings{Yurtsever2015,
Author = {Yurtsever, A. and Tran--Dinh, Q. and Cevher, V.},
Booktitle = {Advances in Neural Information Processing Systems 28},
Date-Added = {2017-10-26 14:30:02 +0000},
Date-Modified = {2017-10-26 14:42:25 +0000},
Title = {A Universal Primal-Dual Convex Optimization Framework},
Year = {2015}}
@conference{locatello2017greedy,
Author = {Locatello, F. and Tschannen, M. and R{\"a}tsch, G. and Jaggi, M.},
Booktitle = {Advances in Neural Information Processing Systems 30},
Date-Modified = {2018-01-08 08:55:53 +0000},
Title = {Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees},
Year = {2017}}
@inproceedings{locatello2017unified,
Author = {Locatello, F. and Khanna, R. and Tschannen, M. and Jaggi, M.},
Booktitle = {Proc. 20th Int. Conf. Artificial Intelligence and Statistics (AISTATS)},
Date-Modified = {2017-11-21 12:42:59 +0000},
Title = {A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe},
Year = {2017}}
@conference{Jaggi2013,
Author = {Jaggi, M.},
Booktitle = {Proceedings of the $30$th International Conference on Machine Learning},
Date-Added = {2017-07-04 22:01:30 +0000},
Date-Modified = {2017-10-31 15:02:13 +0000},
Title = {Revisiting {F}rank--{W}olfe: {P}rojection--free sparse convex optimization},
Year = {2013}}
@article{Freund2016,
Author = {Freund, R. M. and Grigas, P.},
Date-Added = {2017-07-04 21:53:41 +0000},
Date-Modified = {2018-02-06 22:18:55 +0000},
Journal = {Mathematical Programming},
Month = {Jan},
Number = {1},
Pages = {199--230},
Title = {New analysis and results for the {F}rank--{W}olfe method},
Volume = {155},
Year = {2016}}
%%% AE added the following references in Sept 2018
@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}
}
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