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@article{Lofberg2009,
Author = {L\"{o}fberg, Johan},
Date-Added = {2016-10-03 14:09:28 +0000},
Date-Modified = {2016-10-03 14:10:53 +0000},
Journal = {IEEE Trans. Automat. Contr.},
Number = {5},
Pages = {1007--1011},
Title = {Pre- and post-processing sum-of-squares programs in practice},
Volume = {54},
Year = {2009}}
@article{Parrilo2003,
Author = {Parrilo, Pablo A.},
Date-Added = {2016-10-03 14:02:48 +0000},
Date-Modified = {2016-10-03 14:03:41 +0000},
Journal = {Math. Program., Ser. B},
Pages = {293--320},
Title = {Semidefinite programming relaxations for semialgebraic problems},
Volume = {96},
Year = {2003}}
@article{Gouveia2010,
Author = {Gouveia, Jo\~{a}o and Parrilo, Pablo A. and Thomas, Rekha R.},
Date-Added = {2016-10-03 14:01:31 +0000},
Date-Modified = {2016-10-03 14:02:44 +0000},
Journal = {SIAM J. Optim.},
Number = {4},
Pages = {2097--2118},
Title = {Theta bodies for polynomial ideals},
Volume = {20},
Year = {2010}}
@book{Lasserre2015,
Address = {Cambridge, UK},
Author = {Lasserre, Jean Bernard},
Date-Added = {2016-10-03 14:00:07 +0000},
Date-Modified = {2016-10-03 14:01:22 +0000},
Publisher = {Cambridge Univ. Press},
Title = {An introduction to polynomial and semi-algebraic optimization},
Year = {2015}}
@article{Shang2016,
Author = {Shang, Jiangwei and Zhang, Zhengyun and Ng, Hui Khoon},
Date-Added = {2016-10-03 09:32:19 +0000},
Date-Modified = {2016-10-03 09:33:21 +0000},
Note = {arXiv:1609.07881v1 [quant-ph]},
Title = {Superfast maximum likelihood reconstruction for quantum tomography},
Year = {2016}}
@article{Blume-Kohout2010,
Author = {Blume-Kohout, Robin},
Date-Added = {2016-09-15 16:48:33 +0000},
Date-Modified = {2016-09-15 16:49:10 +0000},
Journal = {Phys. Rev. Lett.},
Title = {Hedged maximum likelihood quantum state estimation},
Volume = {105},
Year = {2010}}
@article{Faist2016,
Author = {Faist, Philippe and Renner, Renato},
Date-Added = {2016-09-13 18:05:13 +0000},
Date-Modified = {2016-09-13 18:05:52 +0000},
Journal = {Phys. Rev. Lett.},
Title = {Practical and reliable error bars in quantum tomography},
Volume = {117},
Year = {2016}}
@unpublished{Grant2015,
Author = {Grant, Michael C. and Boyd, Stephen P.},
Date-Added = {2016-09-13 17:46:04 +0000},
Date-Modified = {2016-09-13 17:46:52 +0000},
Note = {Release 2.1},
Title = {The {CVX} user's guide},
Year = {2015}}
@article{Haffner2005,
Author = {H\"{a}ffner, H. and H\"{a}nsel, W. and Roos, C. F. and Benhelm, J. and Check-al-kar, D. and Chwalla, M. and K\"{o}rber, T. and Rapol, U. D. and Riebe, M. and Schmidt, P. O. and Becher, C. and G\"{u}hne, O. and D\"{u}r, W. and Blatt, R.},
Date-Added = {2016-09-13 17:27:13 +0000},
Date-Modified = {2016-09-13 17:29:08 +0000},
Journal = {Nature},
Pages = {643--646},
Title = {Scalable multiparticle entanglement of trapped ions},
Volume = {438},
Year = {2005}}
@article{Endres2003,
Author = {Endres, Dominik M. and Schindelin, Johannes E.},
Date-Added = {2016-09-12 16:53:44 +0000},
Date-Modified = {2016-09-12 16:54:30 +0000},
Journal = {IEEE Trans. Inf. Theory},
Number = {7},
Pages = {1858--1860},
Title = {A new metric for probability distributions},
Volume = {49},
Year = {2003}}
@article{Petz1993,
Author = {Petz, D\'{e}nes and Toth, Gabor},
Date-Added = {2016-09-09 16:57:29 +0000},
Date-Modified = {2016-09-09 16:58:10 +0000},
Journal = {Lett. Math. Phys.},
Pages = {205--216},
Title = {The {B}ogoliubov inner product in quantum statistics},
Volume = {27},
Year = {1993}}
@article{Liu2016,
Author = {Liu, Jing and Yuan, Haidong},
Date-Added = {2016-09-06 16:41:21 +0000},
Date-Modified = {2016-09-06 16:42:02 +0000},
Journal = {New J. Phys.},
Title = {Valid lower bound for all estimators in quantum parameter estimation},
Volume = {18},
Year = {2016}}
@article{Csiszar1998,
Author = {Csisz\'{a}r, Imre},
Date-Added = {2016-09-05 14:52:59 +0000},
Date-Modified = {2016-09-05 14:53:51 +0000},
Journal = {IEEE Trans. Inf. Theory},
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Title = {The method of types},
Volume = {44},
Year = {1998}}
@book{Tomamichel2016,
Address = {Cham},
Author = {Tomamichel, Marco},
Date-Added = {2016-09-05 13:55:44 +0000},
Date-Modified = {2016-09-05 13:56:37 +0000},
Publisher = {Springer},
Title = {Quantum Information Processing with Finite Resources},
Year = {2016}}
@article{Ruskai2013,
Author = {Ruskai, Mary Beth},
Date-Added = {2016-09-01 18:09:58 +0000},
Date-Modified = {2016-09-01 18:10:45 +0000},
Journal = {J. Math. Phys.},
Title = {Remarks on {K}im's strong subadditivity matrix inequality: Extensions and equality conditions},
Volume = {54},
Year = {2013}}
@article{Hansen2003,
Author = {Hansen, Frank and Pedersen, Gert K.},
Date-Added = {2016-09-01 18:08:51 +0000},
Date-Modified = {2016-09-01 18:09:36 +0000},
Journal = {Bull. London Math. Soc.},
Pages = {553--564},
Title = {{J}ensen's operator inequality},
Volume = {35},
Year = {2003}}
@article{Hiai2011,
Author = {Hiai, Fumio and Mosonyi, Mil\'{a}n and Petz, D\'{e}nes and B\'{e}ny, C\'{e}dric},
Date-Added = {2016-09-01 18:06:24 +0000},
Date-Modified = {2016-09-01 18:07:27 +0000},
Journal = {Rev. Math. Phys.},
Number = {7},
Pages = {691--747},
Title = {Quantum $f$-divergences and error correction},
Volume = {23},
Year = {2011}}
@article{Hansen1982,
Author = {Hansen, Frank and Pedersen, Gert Kiargard},
Date-Added = {2016-09-01 18:01:22 +0000},
Date-Modified = {2016-09-01 18:02:20 +0000},
Journal = {Math. Ann.},
Pages = {229--241},
Title = {{J}ensen's inequality for operators and {L}\"{o}wner's theorem},
Volume = {258},
Year = {1982}}
@article{Mond1993,
Author = {Mond, B. and Pe\v{c}ari\'{c}, J. E.},
Date-Added = {2016-08-31 18:46:34 +0000},
Date-Modified = {2016-08-31 18:47:23 +0000},
Journal = {Houston J. Math.},
Number = {3},
Pages = {405--420},
Title = {Convex inequalities in {H}ilbert space},
Volume = {19},
Year = {1993}}
@article{Jaksic2014,
Author = {Jak\v{s}i\'{c}, Rozarija and Pe\v{c}ari\'{c}, Josip},
Date-Added = {2016-08-31 18:42:21 +0000},
Date-Modified = {2016-08-31 18:43:26 +0000},
Journal = {Rend. Circ. Mat. Palermo},
Pages = {1--9},
Title = {Converses of convex inequalities in {H}ilbert space},
Volume = {63},
Year = {2014}}
@article{Peierls1938,
Author = {Peierls, R.},
Date-Added = {2016-08-31 14:13:35 +0000},
Date-Modified = {2016-08-31 14:14:23 +0000},
Journal = {Phys. Rev.},
Pages = {918--919},
Title = {On a minimum property of the free energy},
Volume = {54},
Year = {1938}}
@article{Lieb1975,
Author = {Lieb, Elliott H.},
Date-Added = {2016-08-31 14:09:36 +0000},
Date-Modified = {2016-08-31 14:11:19 +0000},
Journal = {Bull. Am. Math. Soc.},
Number = {1},
Pages = {1--13},
Title = {Some convexity and subadditivity properties of entropy},
Volume = {81},
Year = {1975}}
@article{Vedral2002,
Author = {Vedral, V.},
Date-Added = {2016-08-31 14:02:38 +0000},
Date-Modified = {2016-08-31 14:03:29 +0000},
Journal = {Rev. Mod. Phys.},
Pages = {197--234},
Title = {The role of relative entropy in quantum information theory},
Volume = {74},
Year = {2002}}
@article{Dragomir2003,
Author = {Dragomir, S. S.},
Date-Added = {2016-08-26 13:47:02 +0000},
Date-Modified = {2016-08-26 13:48:27 +0000},
Journal = {J. Inequal. Pure Appl. Math.},
Number = {3},
Title = {A survey on {C}auchy-{B}unyakovsky-{S}chwarz type discrete inequalities},
Volume = {4},
Year = {2003}}
@article{Umegaki1962,
Author = {Umegaki, Hisaharu},
Date-Added = {2016-08-25 17:52:23 +0000},
Date-Modified = {2016-08-25 17:54:56 +0000},
Journal = {Kodai Math. Samin. Rep.},
Number = {2},
Pages = {59--85},
Title = {Conditional expectation in an operator algebra, {IV} (entropy and information)},
Volume = {14},
Year = {1962}}
@article{Davis1959,
Author = {Davis, Chandler},
Date-Added = {2016-08-25 17:47:05 +0000},
Date-Modified = {2016-08-25 17:48:38 +0000},
Journal = {Illinois J. Math.},
Number = {4},
Pages = {538--553},
Title = {Various averaging operations onto subalgebras},
Volume = {3},
Year = {1959}}
@article{Petz2003,
Author = {Petz, D\'{e}nes},
Date-Added = {2016-08-25 16:34:45 +0000},
Date-Modified = {2016-08-25 16:35:38 +0000},
Journal = {Rev. Math. Phys.},
Number = {1},
Pages = {79--91},
Title = {Monotonicity of quantum relative entropy revisited},
Volume = {15},
Year = {2003}}
@book{Hayashi2006,
Address = {Berlin},
Author = {Hayashi, Masahito},
Date-Added = {2016-08-25 14:46:29 +0000},
Date-Modified = {2016-08-25 14:47:19 +0000},
Publisher = {Springer-Verl.},
Title = {Quantum Information: An Introduction},
Year = {2006}}
@article{Bourin2007,
Author = {Bourin, Jean-Christophe and Seo, Yuki},
Date-Added = {2016-08-25 14:15:58 +0000},
Date-Modified = {2016-08-25 14:17:38 +0000},
Journal = {Linear Algebra Appl.},
Pages = {312--316},
Title = {Reverse inequality to {G}olden-{T}hompson type inequalities: Comparison of $\mathrm{e}^{A + B}$ and $\mathrm{e}^A \mathrm{e}^B$},
Volume = {426},
Year = {2007}}
@article{Sutter2016,
Author = {Sutter, David and Berta, Mario and Tomamichel, Marco},
Date-Added = {2016-08-25 14:14:36 +0000},
Date-Modified = {2016-08-25 14:15:19 +0000},
Note = {arXiv:1604.03023v3 [math-ph]},
Title = {Multivariate trace inequalities},
Year = {2016}}
@article{Hayashi2002,
Author = {Hayashi, Masahito},
Date-Added = {2016-08-25 14:11:12 +0000},
Date-Modified = {2016-08-25 14:12:17 +0000},
Journal = {J. Phys. A: Math. Gen.},
Pages = {10759--10773},
Title = {Optimal sequence of quantum measurements in the sense of {S}tein's lemma in quantum hypothesis testing},
Volume = {35},
Year = {2002}}
@book{Bertsekas2016,
Address = {Belmont, MA},
Author = {Bertsekas, Dimitri P.},
Date-Added = {2016-08-23 15:54:32 +0000},
Date-Modified = {2016-09-16 16:41:21 +0000},
Edition = {3rd},
Publisher = {Athena Sci.},
Title = {Nonlinear Programming},
Year = {2016}}
@book{Bratteli1987,
Address = {Berlin},
Author = {Bratteli, O. and Robinson, D. W.},
Date-Added = {2016-08-18 15:32:46 +0000},
Date-Modified = {2016-08-18 15:35:41 +0000},
Edition = {second},
Publisher = {Springer-Verl.},
Title = {Operator Algebras and Quantum Statistical Mechanics 1},
Year = {1987}}
@article{Araki1973,
Author = {Araki, Huzihiro},
Date-Added = {2016-08-18 15:16:26 +0000},
Date-Modified = {2016-08-18 15:17:36 +0000},
Journal = {Commun. Math. Phys.},
Pages = {167--178},
Title = {{G}olden-{T}hompson and {P}eierls-{B}olubov inequalities for a general {v}on~{N}eumann algebra},
Volume = {34},
Year = {1973}}
@article{Bikchentaev2011,
Author = {Bikchentaev, Airat M.},
Date-Added = {2016-08-18 15:14:13 +0000},
Date-Modified = {2016-08-18 15:15:26 +0000},
Journal = {{L}obachevskii J. Math.},
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Pages = {175--179},
Title = {The {P}eierls-{B}oliubov inequality in $C^\ast$-algebras and characterization of tracial functionals},
Volume = {32},
Year = {2011}}
@book{Dixmier1981,
Address = {Amsterdam},
Author = {Dixmier, Jacques},
Date-Added = {2016-08-18 15:08:53 +0000},
Date-Modified = {2016-08-18 15:11:57 +0000},
Publisher = {North-Holland Publ. Co.},
Title = {Von {N}eumann Algebras},
Year = {1981}}
@article{Ruskai1972,
Author = {Ruskai, M. B.},
Date-Added = {2016-08-18 11:52:55 +0000},
Date-Modified = {2016-08-18 11:53:55 +0000},
Journal = {Commun. Math. Phys.},
Pages = {280--289},
Title = {Inequalities for traces on {v}on {N}eumann algebras},
Volume = {26},
Year = {1972}}
@article{Brown1990,
Author = {Brown, Lawrence G. and Kosaki, Hideki},
Date-Added = {2016-08-15 14:20:07 +0000},
Date-Modified = {2016-08-15 14:21:28 +0000},
Journal = {J. Oper. Theory},
Pages = {3--19},
Title = {{J}ensen's inequality in semi-finite {v}on~{N}eumann algebras},
Volume = {23},
Year = {1990}}
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Author = {Furuichi, S. and Yanagi, K. and Kuriyama, K.},
Date-Added = {2016-08-12 13:14:05 +0000},
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Date-Added = {2016-08-11 12:58:57 +0000},
Date-Modified = {2016-08-11 13:00:06 +0000},
Publisher = {Amer. Math. Soc.},
Title = {Trace Ideals and Their Applications},
Year = {2005}}
@book{Ruelle1974,
Address = {Reading, MA},
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Date-Added = {2016-08-10 13:59:25 +0000},
Date-Modified = {2016-08-10 14:00:27 +0000},
Publisher = {W. A. Benjamin, Inc.},
Title = {Statistical Mechanics: Rigorous Results},
Year = {1974}}
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Author = {Wehrl, Alfred},
Date-Added = {2016-08-10 13:45:42 +0000},
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Author = {Carlen, Eric},
Booktitle = {Entropy and the Quantum},
Date-Added = {2016-08-09 16:25:06 +0000},
Date-Modified = {2016-08-09 16:27:44 +0000},
Pages = {73--140},
Publisher = {Amer. Math. Soc.},
Title = {Trace inequalities and quantum entropy: An introductory course},
Year = {2010}}
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Author = {Bebiano, N. and da Provid\^{e}ncia Jr., J. and Lemos R.},
Date-Added = {2016-08-08 14:02:10 +0000},
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Title = {Matrix inequalities in statistical mechanics},
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Author = {Nesterov, {Yu.} and Tun{\c{c}}el, L.},
Date-Added = {2016-08-05 16:26:44 +0000},
Date-Modified = {2016-08-05 16:29:22 +0000},
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Year = {2016}}
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Author = {He, Niao and Harchaoui, Zaid and Wang, Yichen and Song, Le},
Date-Added = {2016-08-05 15:29:44 +0000},
Date-Modified = {2016-08-05 15:30:35 +0000},
Note = {arXiv:1608.01264v1 [cs.LG]},
Title = {Fast and simple optimization for {P}oisson likelihood models},
Year = {2016}}
@article{Patil2016,
Author = {Patil, Sukanya and Rajwade, Ajit},
Date-Added = {2016-08-05 14:42:30 +0000},
Date-Modified = {2016-08-05 14:43:48 +0000},
Note = {arXiv:1606.08557v1 [cs.IT]},
Title = {Reconstruction error bounds for compressed sensing under {P}oisson noise using the square root of the {J}ensen-{S}hannon divergence},
Year = {2016}}
@book{Heinosaari2012,
Address = {Cambridge, UK},
Author = {Heinosaari, Teiko and Ziman, M\'{a}rio},
Date-Added = {2016-07-28 16:04:44 +0000},
Date-Modified = {2016-07-28 16:05:58 +0000},
Publisher = {Cambridge Univ. Press},
Title = {The Mathematical Language of Quantum Theory},
Year = {2012}}
@article{Tseng2010,
Author = {Tseng, Paul},
Date-Added = {2016-07-28 14:15:53 +0000},
Date-Modified = {2016-07-28 14:16:46 +0000},
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Title = {Approximation accuracy, gradient methods, and error bounds for structured convex optimization},
Volume = {125},
Year = {2010}}
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Author = {G\"{u}ler, Osman},
Date-Added = {2016-07-28 13:53:23 +0000},
Date-Modified = {2016-07-28 13:54:21 +0000},
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Number = {4},
Pages = {649--664},
Title = {New proximal point algorithms for convex minimization},
Volume = {2},
Year = {1992}}
@incollection{Nesterov2010,
Author = {Nesterov, Yurii},
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Date-Added = {2016-07-26 17:18:06 +0000},
Date-Modified = {2016-07-26 17:19:10 +0000},
Editor = {Cochran, James J.},
Publisher = {John Wiley \& Sons},
Title = {Subgradient optimization},
Year = {2010}}
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Author = {Gasnikov, A. V. and Gasnikova, E. B. and Nesterov, {Yu.} E. and Chernov, A. V.},
Date-Added = {2016-07-26 16:24:20 +0000},
Date-Modified = {2016-07-26 16:25:36 +0000},
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Title = {Efficient numerical methods for entropy-linear programming problems},
Volume = {56},
Year = {2016}}
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Date-Added = {2016-07-22 13:47:52 +0000},
Date-Modified = {2016-07-22 13:49:13 +0000},
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Date-Added = {2016-07-15 14:08:37 +0000},
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@book{Zeidler1985,
Address = {New York, NY},
Author = {Zeidler, Eberhard},
Date-Added = {2016-07-14 17:34:29 +0000},
Date-Modified = {2016-07-14 17:35:38 +0000},
Publisher = {Springer},
Title = {Nonlinear Functional Analysis and its Applications III: Variational Methods and Optimization},
Year = {1985}}
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Date-Added = {2016-07-11 14:03:29 +0000},
Date-Modified = {2016-07-11 14:04:12 +0000},
Journal = {Inverse Probl.},
Pages = {1411--1421},
Title = {Convergence rates of convex variational regularization},
Volume = {20},
Year = {2004}}
@book{Bertsekas1999,
Address = {Belmont, MA},
Author = {Bertsekas, Dimitri P.},
Date-Added = {2016-07-08 17:52:15 +0000},
Date-Modified = {2016-07-08 17:52:59 +0000},
Publisher = {Athena Scientific},
Title = {Nonlinear Programming},
Year = {1999}}
@article{Adler1989,
Author = {Adler, Ilan and Resende, Mauricio G. C. and Veiga, Geraldo and Karmarkar, Narendra},
Date-Added = {2016-07-07 15:44:47 +0000},
Date-Modified = {2016-07-07 15:45:52 +0000},
Journal = {Math. Program.},
Pages = {297--335},
Title = {An implementation of {K}armarkar's algorithm for linear programming},
Volume = {44},
Year = {1989}}
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Author = {Zhivotovskiy, Nikita and Hanneke, Steve},
Date-Added = {2016-07-07 15:27:35 +0000},
Date-Modified = {2016-07-07 15:28:39 +0000},
Note = {arXiv:1606.00922v1 [math.ST]},
Title = {Localization of {VC} classes: Beyond local {R}ademacher complexities},
Year = {2016}}
@article{Karmarkar1984a,
Author = {Karmarkar, N.},
Date-Added = {2016-07-06 15:19:13 +0000},
Date-Modified = {2016-07-06 15:20:03 +0000},
Journal = {Combinatorica},
Number = {4},
Pages = {373--395},
Title = {A new polynomial-time algorithm for linear programming},
Volume = {4},
Year = {1984}}
@article{Nesterov1997,
Author = {Nesterov, {Yu.}},
Date-Added = {2016-07-06 14:02:18 +0000},
Date-Modified = {2016-07-06 14:03:14 +0000},
Journal = {Math. Program.},
Pages = {285--297},
Title = {Interior-point methods: An old and new approach to nonlinear programming},
Volume = {79},
Year = {1997}}
@unpublished{Ledoux2016,
Author = {Ledoux, Michel},
Date-Added = {2016-07-05 12:07:42 +0000},
Date-Modified = {2016-07-05 12:08:05 +0000},
Title = {The {MMSE} conjecture},
Year = {2016}}
@article{Lacoste-Julien2016,
Author = {Lacoste-Julien, Simon},
Date-Added = {2016-07-04 13:08:33 +0000},
Date-Modified = {2016-07-04 13:10:59 +0000},
Note = {arXiv:1607.00345v1 [math.OC]},
Title = {Convergence rate of {F}rank-{W}olfe for non-convex objectives},
Year = {2016}}
@inproceedings{Hazan2012,
Author = {Hazan, Elad},
Booktitle = {Proc. 29th Int. Conf. Machine Learning},
Date-Added = {2016-07-01 16:34:39 +0000},
Date-Modified = {2016-07-01 16:35:18 +0000},
Title = {Projection-free online learning},
Year = {2012}}
@inproceedings{Lacoste-Julien2015,
Author = {Lacoste-Julien, Simon and Jaggi, Martin},
Booktitle = {Adv. Neural Information Processing Systems 28},
Date-Added = {2016-06-30 14:39:56 +0000},
Date-Modified = {2016-06-30 14:41:03 +0000},
Title = {On the global linear convergence of {F}rank-{W}olfe optimization variants},
Year = {2015}}
@article{Verger-Gaugry2005,
Author = {Verger-Gaugry, Jean-Louis},
Date-Added = {2016-06-30 12:20:26 +0000},
Date-Modified = {2016-06-30 12:21:22 +0000},
Journal = {Discrete Comput. Geom.},
Pages = {143--155},
Title = {Covering a ball with smaller equal balls in $\mathbb{R}^n$},
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