%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Joel Tropp at 2016-07-27 16:30:08 -0700 %% Saved with string encoding Unicode (UTF-8) @unpublished{TYUC16:Randomized-Single-View, Author = {J. A. Tropp and A. Yurtsever and M.~Udell and V.~Cevher}, Date-Added = {2016-07-27 23:25:51 +0000}, Date-Modified = {2016-07-27 23:30:06 +0000}, Month = {Aug.}, Note = {Available at \url{http://arXiv.org/abs/1508.xxxxx}}, Title = {Randomized single-view algorithms for low-rank matrix reconstruction}, Year = {2016}} @unpublished{EM15:Convergence-Rates, Author = {M. A. Erdogdu and A. Montanari}, Date-Added = {2016-05-20 02:22:18 +0000}, Date-Modified = {2016-05-20 02:23:09 +0000}, Month = {Aug.}, Note = {Available at \url{http://arXiv.org/abs/1508.02810}}, Title = {Convergence rates of sub-sampled {N}ewton methods}, Year = {2015}} @unpublished{PW15:Newton-Sketch, Author = {M. Pilanci and M. Wainwright}, Date-Added = {2016-05-20 02:20:40 +0000}, Date-Modified = {2016-05-20 02:21:28 +0000}, Month = {May}, Note = {Available at \url{http://arXiv.org/abs/1505.02250}}, Title = {Newton sketch: A linear-time optimization algorithm with linear-quadratic convergence}, Year = {2015}} @article{Mut08:Data-Streams, Author = {Muthukrishnan, S.}, Date-Added = {2016-05-20 01:41:12 +0000}, Date-Modified = {2016-05-20 04:33:19 +0000}, Fjournal = {Foundations and Trends${}\sp \circledR$ in Theoretical Computer Science}, Journal = {Found. Trends Theor. Comput. Sci.}, Mrclass = {68P20 (68M10 68Q17 68Q25 68W20 68W25)}, Mrnumber = {2379507}, Mrreviewer = {Hsien-Kuei Hwang}, Number = {2}, Pages = {117--236}, Title = {Data streams: algorithms and applications}, Volume = {1}, Year = {2005}, Bdsk-Url-1 = {http://dx.doi.org/10.1561/0400000002}} @article{Roc76:Monotone-Operators, Author = {Rockafellar, R. T.}, Date-Added = {2016-05-20 00:56:27 +0000}, Date-Modified = {2016-05-20 04:52:44 +0000}, Fjournal = {SIAM Journal on Control and Optimization}, Journal = {SIAM J. Control Optimization}, Mrclass = {47H05 (49D45)}, Mrnumber = {0410483}, Mrreviewer = {G. M. Ewing}, Number = {5}, Pages = {877--898}, Title = {Monotone operators and the proximal point algorithm}, Volume = {14}, Year = {1976}} @inproceedings{OLY+16:Frank-Wolfe-Works, Abstract = {We study a phase retrieval problem in the Poisson noise model. Motivated by the PhaseLift approach, we approximate the maximum-likelihood estimator by solving a convex program with a nuclear norm constraint. While the Frank-Wolfe algorithm, together with the Lanczos method, can efficiently deal with nuclear norm constraints, our objective function does not have a Lipschitz continuous gradient, and hence existing convergence guarantees for the Frank-Wolfe algorithm do not apply. In this paper, we show that the Frank-Wolfe algorithm works for the Poisson phase retrieval problem, and has a global convergence rate of O(1/t), where t is the iteration counter. We provide rigorous theoretical guarantee and illustrating numerical results.}, Affiliation = {EPFL}, Author = {G. Odor and Y.-H. Li and A. Yurtsever and Y.-P. Hsieh and Q. Tran-Dinh and M. El Halabi and V. Cevher}, Booktitle = {41{s}t {IEEE} {I}ntl. {C}onf. {A}coustics, {S}peech and {S}ignal {P}rocessing (ICASSP)}, Date-Added = {2016-05-19 23:58:33 +0000}, Date-Modified = {2016-05-20 04:51:28 +0000}, Details = {http://infoscience.epfl.ch/record/215495}, Documenturl = {http://infoscience.epfl.ch/record/215495/files/fw4ppr.pdf}, Keywords = {Phase retrieval; Poisson noise; PhaseLift; Frank-Wolfe algorithm; Non-Lipschitz continuous gradient}, Oai-Id = {oai:infoscience.epfl.ch:215495}, Oai-Set = {conf}, Review = {REVIEWED}, Status = {ACCEPTED}, Submitter = {221971}, Title = {{F}rank-{W}olfe works for non-{L}ipschitz continuous gradient objectives: scalable {P}oisson phase retrieval}, Unit = {LIONS}, Year = 2016} @article{AT06:Interior-Gradient, Author = {A. Auslender and M. Teboulle}, Date-Added = {2016-05-19 21:59:38 +0000}, Date-Modified = {2016-05-20 04:48:47 +0000}, Journal = {SIAM J. Optim.}, Mrclass = {90C25 (90C22 90C30)}, Mrnumber = {2197553}, Mrreviewer = {Etienne de Klerk}, Number = {3}, Pages = {697--725 (electronic)}, Title = {Interior gradient and proximal methods for convex and conic optimization}, Volume = {16}, Year = {2006}, Bdsk-Url-1 = {http://dx.doi.org/10.1137/S1052623403427823}} @article{CETV13:Phase-Retrieval, Author = {E. J. Cand{\`e}s and Y. C. Eldar and T. Strohmer and V. Voroninski}, Coden = {SJISBI}, Date-Added = {2016-05-19 20:47:23 +0000}, Date-Modified = {2016-05-20 05:13:53 +0000}, Fjournal = {SIAM Journal on Imaging Sciences}, Journal = {SIAM J. Imaging Sci.}, Mrclass = {94A08 (42A38 90C25)}, Mrnumber = {3032952}, Number = {1}, Pages = {199--225}, Title = {Phase retrieval via matrix completion}, Volume = {6}, Year = {2013}, Bdsk-Url-1 = {http://dx.doi.org/10.1137/110848074}} @article{BBCE09:Painless-Reconstruction, Author = {R. Balan and B. G. Bodmann and P. G. Casazza and D. Edidin}, Date-Added = {2016-05-19 20:41:45 +0000}, Date-Modified = {2016-05-20 04:30:39 +0000}, Fjournal = {The Journal of Fourier Analysis and Applications}, Journal = {J. Fourier Anal. Appl.}, Mrclass = {42C15 (94A12)}, Mrnumber = {2549940}, Mrreviewer = {Alberto Portal}, Number = {4}, Pages = {488--501}, Title = {Painless reconstruction from magnitudes of frame coefficients}, Volume = {15}, Year = {2009}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00041-009-9065-1}} @article{CLS15:Phase-Retrieval, Author = {E. J. Cand{\`e}s and X. Li and M. Soltanolkoltabi}, Date-Added = {2016-05-19 20:36:47 +0000}, Date-Modified = {2016-05-19 20:39:24 +0000}, Journal = {IEEE Trans. Inform. Theory}, Number = {4}, Pages = {1985--2007}, Title = {Phase retrieval via {W}irtinger {F}low: Theory and algorithms}, Volume = {61}, Year = {2015}} @article{GS72:Practical-Algorithm, Author = {R. W. Gerchberg and W. O. Saxton}, Date-Added = {2016-05-19 20:35:32 +0000}, Date-Modified = {2016-05-19 20:36:22 +0000}, Journal = {Optik}, Number = {237--246}, Title = {A practical algorithm for the determination of the phase from image and diffraction plane pictures}, Volume = {35}, Year = {1972}} @article{HCO+15:Solving-Ptychography, Abstract = {Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that currently solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the ptychographic reconstruction algorithm that is currently in widespread use.}, Author = {R. Horstmeyer and R. Y. Chen and X. Ou and B. Ames and J. A. Tropp and C. Yang}, Date-Added = {2016-05-19 01:43:25 +0000}, Date-Modified = {2016-05-20 04:32:37 +0000}, Journal = {New Journal of Physics}, Number = {5}, Pages = {053044}, Title = {Solving ptychography with a convex relaxation}, Volume = {17}, Year = {2015}, Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/17/i=5/a=053044}} @incollection{Hig89:Matrix-Nearness, Author = {Higham, N. J.}, Booktitle = {Applications of matrix theory ({B}radford, 1988)}, Date-Added = {2016-05-19 01:42:03 +0000}, Date-Modified = {2016-05-20 04:50:04 +0000}, Mrclass = {65F30 (15A57)}, Mrnumber = {1041063}, Mrreviewer = {F. Szidarovszky}, Pages = {1--27}, Publisher = {Oxford Univ. Press, New York}, Title = {Matrix nearness problems and applications}, Year = {1989}, Bdsk-Url-1 = {http://dx.doi.org/10.1093/imamat/22.1.1}} @phdthesis{Faz02:Matrix-Rank, Address = {Palo Alto}, Author = {M. Fazel}, Date-Added = {2016-05-18 22:53:41 +0000}, Date-Modified = {2016-05-20 04:49:21 +0000}, School = {Stanford Univ.}, Title = {Matrix rank minimization with applications}, Type = {Ph{D} {D}issertation}, Year = {2002}} @inproceedings{YHC15:Scalable-Convex, Abstract = {This paper describes scalable convex optimization methods for phase retrieval. The main characteristics of these methods are the cheap per-iteration complexity and the low-memory footprint. With a variant of the original PhaseLift formulation, we first illustrate how to leverage the scalable Frank-Wolfe (FW) method (also known as the conditional gradient algorithm), which requires a tuning parameter. We demonstrate that we can estimate the tuning parameter of the FW algorithm directly from the measurements, with rigorous theoretical guarantees. We then illustrate numerically that recent advances in universal primal-dual convex optimization methods offer significant scalability improvements over the FW method, by recovering full HD resolution color images from their quadratic measurements.}, Affiliation = {EPFL}, Author = {Yurtsever, A. and Hsieh, Y.-P. and Cevher, V.}, Booktitle = {6{t}h {IEEE} {I}ntl. {W}orkshop on {C}omputational {A}dvances in {M}ulti-{S}ensor {A}daptive {P}rocessing ({CAMSAP})}, Date-Added = {2016-05-06 22:50:11 +0000}, Date-Modified = {2016-05-20 07:01:30 +0000}, Details = {http://infoscience.epfl.ch/record/212914}, Documenturl = {http://infoscience.epfl.ch/record/212914/files/ScalableConvexMethodsForPhaseRetrieval.pdf}, Keywords = {phase retrieval; PhaseLift; scalable convex methods; Frank-Wolfe; universal primal dual convex optimization methods}, Location = {Cancun, Mexico}, Oai-Id = {oai:infoscience.epfl.ch:212914}, Oai-Set = {conf}, Review = {REVIEWED}, Status = {ACCEPTED}, Submitter = {233086}, Title = {Scalable convex methods for phase retrieval}, Unit = {LIONS}, Year = 2015} @unpublished{RSW15:Conditional-Gradient, Author = {N. Rao and P. Shah and S. Wright}, Date-Added = {2016-05-06 22:45:44 +0000}, Date-Modified = {2016-05-06 22:47:42 +0000}, Note = {Available at \url{http://people.inf.ethz.ch/jaggim/NIPS-workshop-FW-greedy/papers/rao_shah_wright_final.pdf}}, Title = {Conditional gradient with enhancement and truncation for atomic-norm regularization}, Year = {2015}} @inproceedings{SGS11:Large-Scale-Convex, Author = {S. Shalev-Schwartz and A. Gonen and O. Shamir}, Booktitle = {Proc. 28th Intl. Conf. Machine Learning}, Date-Added = {2016-05-06 22:44:53 +0000}, Date-Modified = {2016-05-06 22:45:29 +0000}, Title = {Large-scale convex minimization with a low-rank constraint}, Year = {2011}} @unpublished{ABH16:Second-Order-Stochastic, Author = {N. Agarwal, B. Bullins, E. Hazan}, Date-Added = {2016-05-06 22:42:44 +0000}, Date-Modified = {2016-05-20 07:00:32 +0000}, Month = {Feb.}, Note = {Available at \url{http://arXiv.org/abs/1602.03943}}, Title = {Second-Order Stochastic Optimization in Linear Time}, Year = {2016}} @article{GH15:Sublinear-Time, Author = {D. Garber and E. Hazan}, Date-Added = {2016-05-06 22:35:00 +0000}, Date-Modified = {2016-05-06 22:36:22 +0000}, Doi = {10.1007/s10107-015-0932-z}, Journal = {Math. Program. Ser. A}, Title = {Sublinear time algorithms for approimate semidefinite programming}, Year = {2015}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10107-015-0932-z}} @unpublished{JNS12:Low-Rank-Matrix, Author = {P. Jain and P. Netrapalli and S. Sanghavi}, Date-Added = {2016-05-06 22:29:08 +0000}, Date-Modified = {2016-05-06 22:29:57 +0000}, Month = {Dec.}, Note = {Available at \url{http://arXiv.org/abs/1212.0467}}, Title = {Low-rank matrix completion using alternating minimization}, Year = {2012}} @unpublished{BKS15:Dropping-Convexity, Author = {S. Bhojanapalli and A. Kyrillidis and S. Sanghavi}, Date-Added = {2016-05-06 22:27:48 +0000}, Date-Modified = {2016-05-06 22:28:48 +0000}, Month = {Sep.}, Note = {Available at \url{http://arXiv.org/abs/1509.03917}}, Title = {Dropping convexity for faster semi-definite optimization}, Year = {2015}} @unpublished{Bou15:Riemannian-Low-Rank, Author = {N. Boumal}, Date-Added = {2016-05-06 22:25:45 +0000}, Date-Modified = {2016-05-06 22:27:03 +0000}, Month = {June}, Note = {Available at \url{http://arXiv.org/abs/1506.00575}}, Title = {A {R}iemannian low-rank method for optimization over semidefinite matrices with block-diagonal constraints}, Year = {2015}} @article{BM03:Nonlinear-Programming, Author = {Burer, S. and Monteiro, R. D. C.}, Date-Added = {2016-05-06 22:19:12 +0000}, Date-Modified = {2016-05-20 04:31:27 +0000}, Fjournal = {Mathematical Programming. A Publication of the Mathematical Programming Society}, Journal = {Math. Program.}, Mrclass = {90C22 (90C30)}, Mrnumber = {1976484}, Mrreviewer = {Zheng Hai Huang}, Number = {2, Ser. B}, Pages = {329--357}, Title = {A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization}, Volume = {95}, Year = {2003}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10107-002-0352-8}} @inproceedings{Haz08:Sparse-Approximate, Address = {Rio de Janeiro}, Author = {E. Hazan}, Booktitle = {Proc. 8th Latin American Theoretical Informatics Symposium (LATIN)}, Date-Added = {2016-05-02 19:54:03 +0000}, Date-Modified = {2016-05-02 19:55:26 +0000}, Month = {Apr.}, Title = {Sparse approximate solutions to semidefinite programs}, Year = {2008}} @unpublished{Upa16:Fast-Space-Optimal, Author = {J. Upadhyay}, Date-Added = {2016-05-02 19:48:41 +0000}, Date-Modified = {2016-05-02 19:51:25 +0000}, Month = {Apr.}, Note = {Available at \url{http://arXiv.org/abs/1604.01429}}, Title = {Fast and Space-optimal Low-rank Factorization in the Streaming Model With Application in Differential Privacy}, Year = {2016}} @inproceedings{BWZ15:Optimal-Principal, Address = {Cambridge, MA}, Author = {C. Boutsidis and D. Woodruff and P. Zhong}, Booktitle = {Proc. 2016 ACM Symp. Theory of Computing (STOC)}, Date-Added = {2016-05-02 19:40:18 +0000}, Date-Modified = {2016-05-20 04:31:02 +0000}, Title = {Optimal principal component analysis in distributed and streaming models}, Year = {2016}} @article{NW12:Restricted-Strong, Author = {S. Negahban and M. J. Wainwright}, Date-Added = {2016-05-02 19:39:30 +0000}, Date-Modified = {2016-05-20 04:35:03 +0000}, Fjournal = {Journal of Machine Learning Research (JMLR)}, Journal = {J. Mach. Learn. Res.}, Mrclass = {62H12 (15A83 60B20 60E15 62G20)}, Mrnumber = {2930649}, Pages = {1665--1697}, Title = {Restricted strong convexity and weighted matrix completion: optimal bounds with noise}, Volume = {13}, Year = {2012}} @article{PW15:Randomized-Sketches, Author = {M. Pilanci and M. J. Wainwright}, Date-Added = {2016-05-02 19:39:30 +0000}, Date-Modified = {2016-05-20 04:39:02 +0000}, Fjournal = {Institute of Electrical and Electronics Engineers. Transactions on Information Theory}, Journal = {IEEE Trans. Inform. Theory}, Mrclass = {94A12}, Mrnumber = {3386504}, Number = {9}, Pages = {5096--5115}, Title = {Randomized sketches of convex programs with sharp guarantees}, Volume = {61}, Year = {2015}} @inproceedings{Sar06:Improved-Approximation, Address = {Berkeley}, Author = {T. Sarl{\'o}s}, Booktitle = {Proc. 47th Ann. IEEE Symposium on Foundations of Computer Science (FOCS)}, Date-Added = {2016-05-02 19:37:34 +0000}, Date-Modified = {2016-05-02 19:38:47 +0000}, Title = {Improved approximation algorithms for large matrices via random projections}, Year = {2006}} @inproceedings{CW09:Numerical-Linear, Address = {Bethesda}, Author = {K. L. Clarkson and D. P. Woodruff}, Booktitle = {Proc. 41st ACM Symposium on Theory of Computing (STOC)}, Date-Added = {2016-05-02 19:34:04 +0000}, Date-Modified = {2016-05-02 19:58:30 +0000}, Title = {Numerical linear algebra in the streaming model}, Year = {2009}} @article{Mah11:Randomized-Algorithms, Author = {M. W. Mahoney}, Date-Added = {2016-05-02 19:31:31 +0000}, Date-Modified = {2016-05-20 04:33:07 +0000}, Journal = {Foundations and Trends{\textregistered} in Machine Learning}, Number = {2}, Pages = {123-224}, Title = {Randomized Algorithms for Matrices and Data}, Volume = {3}, Year = {2011}, Bdsk-Url-1 = {http://dx.doi.org/10.1561/2200000035}} @inproceedings{Jag13:Revisiting-Frank-Wolfe, Address = {Atlanta}, Author = {M. Jaggi}, Booktitle = {Proc. 30th Intl. Conf. Machine Learning (ICML)}, Date-Added = {2016-05-02 19:29:35 +0000}, Date-Modified = {2016-05-02 19:30:41 +0000}, Title = {Revisiting {F}rank--{W}olfe: Projection-free sparse convex optimization}, Year = {2013}} @article{Woo14:Sketching-Tool, Author = {D. P. Woodruff}, Date-Added = {2016-05-02 19:27:08 +0000}, Date-Modified = {2016-05-20 04:38:49 +0000}, Fjournal = {Foundations and Trends${}\sp \circledR$ in Theoretical Computer Science}, Journal = {Found. Trends Theor. Comput. Sci.}, Mrclass = {65F99 (15-02)}, Mrnumber = {3285427}, Number = {1-2}, Pages = {iv+157}, Title = {Sketching as a tool for numerical linear algebra}, Volume = {10}, Year = {2014}} @article{WLRT08:Fast-Randomized, Author = {F. Woolfe and E. Liberty and V. Rokhlin and M. Tygert}, Date-Added = {2016-05-02 19:27:08 +0000}, Date-Modified = {2016-05-20 04:33:58 +0000}, Fjournal = {Applied and Computational Harmonic Analysis. Time-Frequency and Time-Scale Analysis, Wavelets, Numerical Algorithms, and Applications}, Journal = {Appl. Comput. Harmon. Anal.}, Mrclass = {15A03 (15A18 15A52 65F30)}, Mrnumber = {2455599}, Mrreviewer = {Hans Havlicek}, Number = {3}, Pages = {335--366}, Title = {A fast randomized algorithm for the approximation of matrices}, Volume = {25}, Year = {2008}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.acha.2007.12.002}} @article{HMT11:Finding-Structure, Author = {Halko, N. and Martinsson, P. G. and Tropp, J. A.}, Coden = {SIREAD}, Date-Added = {2016-05-02 19:24:04 +0000}, Date-Modified = {2016-05-20 04:32:09 +0000}, Fjournal = {SIAM Review}, Journal = {SIAM Rev.}, Mrclass = {65F30 (60B20 68W20)}, Mrnumber = {2806637}, Mrreviewer = {Thomas K. Huckle}, Number = {2}, Pages = {217--288}, Title = {Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions}, Volume = {53}, Year = {2011}, Bdsk-Url-1 = {http://dx.doi.org/10.1137/090771806}} @unpublished{YZS14:Generalized-Conditional, Author = {Y. Yu and X. Zhang and D. Schuurmans}, Date-Added = {2016-05-02 19:19:19 +0000}, Date-Modified = {2016-05-02 19:23:06 +0000}, Note = {Available at \url{http://arXiv.org/abs/1410.4828}}, Title = {Generalized conditional gradient for sparse estimation}, Year = {2014}} @inproceedings{YTC15:Universal-Primal-Dual, Address = {Montr{\'e}al}, Author = {A. Yurtsever and Q. Tran-Dinh and V. Cevher}, Booktitle = {Proc. 29th Ann. Conf. Neural Information Processings (NIPS)}, Date-Added = {2016-05-02 19:17:36 +0000}, Date-Modified = {2016-05-02 21:52:01 +0000}, Title = {A universal primal--dual convex optimization framework}, Year = {2015}} @unpublished{CTUY16:Storage-Optimal-Algorithms, Author = {V. Cevher and J. A. Tropp and M. Udell and A. Yurtsever}, Date-Added = {2016-05-02 19:14:55 +0000}, Date-Modified = {2016-05-02 19:17:07 +0000}, Month = {May}, Note = {In preparation}, Title = {Storage-optimal algorithms for semidefinite programs with low-rank solutions}, Year = {2016}} @article{Cla10:Coresets-Sparse, Author = {Clarkson, K. L.}, Date-Added = {2016-05-02 19:08:48 +0000}, Date-Modified = {2016-05-20 04:31:40 +0000}, Fjournal = {ACM Transactions on Algorithms}, Journal = {ACM Trans. Algorithms}, Mrclass = {90C25 (68T05 90C55)}, Mrnumber = {2760426}, Number = {4}, Pages = {Art. 63, 30}, Title = {Coresets, sparse greedy approximation, and the {F}rank-{W}olfe algorithm}, Volume = {6}, Year = {2010}, Bdsk-Url-1 = {http://dx.doi.org/10.1145/1824777.1824783}} @techreport{Nes15:Complexity-Bounds, Author = {Yu. Nesterov}, Date-Added = {2016-05-02 19:03:30 +0000}, Date-Modified = {2016-05-02 19:04:48 +0000}, Institution = {Catholic University of Louvain}, Month = {Feb.}, Number = {2015/03}, Title = {Complexity bounds for primal-dual methods minimizing the model of objective function}, Type = {CORE discussion paper}, Year = {2015}} @article{FW56:Algorithm-Quadratic, Author = {M. Frank and P. Wolfe}, Date-Added = {2016-05-02 19:00:32 +0000}, Date-Modified = {2016-05-20 04:49:39 +0000}, Fjournal = {Naval Research Logistics Quarterly}, Journal = {Naval Res. Logist. Quart.}, Mrclass = {90.0X}, Mrnumber = {0089102}, Pages = {95--110}, Title = {An algorithm for quadratic programming}, Volume = {3}, Year = {1956}} @article{JN16:Solving-Variational, Author = {A. Juditsky and A. Nemirovski}, Date-Added = {2016-05-02 19:00:32 +0000}, Date-Modified = {2016-05-20 04:35:10 +0000}, Fjournal = {Mathematical Programming. A Publication of the Mathematical Optimization Society}, Journal = {Math. Program.}, Mrclass = {65K15 (68T10 90C25 90C47)}, Mrnumber = {3459200}, Number = {1-2, Ser. A}, Pages = {221--256}, Title = {Solving variational inequalities with monotone operators on domains given by {L}inear {M}inimization {O}racles}, Volume = {156}, Year = {2016}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10107-015-0876-3}} @article{LP66:Minimization-Methods, Author = {Levitin, E. S. and Poljak, B. T.}, Date-Added = {2016-05-02 19:00:32 +0000}, Date-Modified = {2016-05-02 19:01:01 +0000}, Fjournal = {Akademija Nauk SSSR. \v Zurnal Vy\v cislitel\cprime no\u\i\ Matematiki i Matemati\v cesko\u\i\ Fiziki}, Issn = {0044-4669}, Journal = {\v Z. Vy\v cisl. Mat. i Mat. Fiz.}, Mrclass = {65.30 (90.00)}, Mrnumber = {0211590}, Mrreviewer = {J. S. Shipman}, Pages = {787--823}, Title = {Minimization methods in the presence of constraints}, Volume = {6}, Year = {1966}}