{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:41:45Z","timestamp":1740109305189,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:00:00Z","timestamp":1648771200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:00:00Z","timestamp":1648771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2023,3]]},"DOI":"10.1007\/s10107-022-01795-7","type":"journal-article","created":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T15:26:27Z","timestamp":1648826787000},"page":"733-785","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones"],"prefix":"10.1007","volume":"198","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5489-8213","authenticated-orcid":false,"given":"Dogyoon","family":"Song","sequence":"first","affiliation":[]},{"given":"Pablo A.","family":"Parrilo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,4,1]]},"reference":[{"key":"1795_CR1","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.disopt.2016.04.004","volume":"24","author":"AA Ahmadi","year":"2017","unstructured":"Ahmadi, A.A., Dash, S., Hall, G.: Optimization over structured subsets of positive semidefinite matrices via column generation. Discrete Optim. 24, 129\u2013151 (2017)","journal-title":"Discrete Optim."},{"key":"1795_CR2","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1090\/conm\/685\/13712","volume":"685","author":"AA Ahmadi","year":"2017","unstructured":"Ahmadi, A.A., Hall, G.: Sum of squares basis pursuit with linear and second order cone programming. Algebraic Geom. Methods Discrete Math. 685, 27\u201353 (2017)","journal-title":"Algebraic Geom. Methods Discrete Math."},{"issue":"2","key":"1795_CR3","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1137\/18M118935X","volume":"3","author":"AA Ahmadi","year":"2019","unstructured":"Ahmadi, A.A., Majumdar, A.: DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization. SIAM J. Appl. Algebra Geom. 3(2), 193\u2013230 (2019)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"1795_CR4","doi-asserted-by":"crossref","unstructured":"Aubrun, G., Szarek, S.: Dvoretzky\u2019s theorem and the complexity of entanglement detection. Discrete Analysis, pp. 1242 (2017)","DOI":"10.19086\/da.1242"},{"key":"1795_CR5","doi-asserted-by":"crossref","DOI":"10.1090\/surv\/223","volume-title":"Alice and Bob Meet Banach","author":"G Aubrun","year":"2017","unstructured":"Aubrun, G., Szarek, S.J.: Alice and Bob Meet Banach, vol. 223. American Mathematical Society, Providence (2017)"},{"key":"1795_CR6","doi-asserted-by":"publisher","first-page":"159","DOI":"10.2307\/1970980","volume":"102","author":"W Beckner","year":"1975","unstructured":"Beckner, W.: Inequalities in Fourier analysis. Ann. Math. 102, 159\u2013182 (1975)","journal-title":"Ann. Math."},{"key":"1795_CR7","doi-asserted-by":"crossref","unstructured":"Blekherman, G., Dey, S.S., Molinaro, M., Sun, S.: Sparse PSD approximation of the PSD cone. Math. Program. 191, 981\u20131004 (2022)","DOI":"10.1007\/s10107-020-01578-y"},{"key":"1795_CR8","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.laa.2005.03.029","volume":"405","author":"EG Boman","year":"2005","unstructured":"Boman, E.G., Chen, D., Parekh, O., Toledo, S.: On factor width and symmetric H-matrices. Linear Algebra Appl. 405, 239\u2013248 (2005)","journal-title":"Linear Algebra Appl."},{"key":"1795_CR9","doi-asserted-by":"crossref","unstructured":"Bonami, A.: \u00c9tude des coefficients de Fourier des fonctions de $$ L^{p} (G)$$. In: Annales de l\u2019Institut Fourier, vol. 20, pp. 335\u2013402. (1970)","DOI":"10.5802\/aif.357"},{"key":"1795_CR10","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199535255.001.0001","volume-title":"Concentration Inequalities: A Nonasymptotic Theory of Independence","author":"S Boucheron","year":"2013","unstructured":"Boucheron, S., Lugosi, G., Massart, P.: Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press, Oxford (2013)"},{"issue":"4","key":"1795_CR11","doi-asserted-by":"publisher","first-page":"1479","DOI":"10.1287\/moor.2020.1077","volume":"46","author":"H Fawzi","year":"2021","unstructured":"Fawzi, H.: On polyhedral approximations of the positive semidefinite cone. Math. Oper. Res. 46(4), 1479\u20131489 (2021)","journal-title":"Math. Oper. Res."},{"key":"1795_CR12","unstructured":"Fawzi, H., Gouveia, J., Parrilo, P.A., Saunderson, J., Thomas, R.R.: Lifting for simplicity: concise descriptions of convex sets. arXiv preprint arXiv:2002.09788 (2020)"},{"key":"1795_CR13","unstructured":"Fawzi, H., Parrilo, P.A.: Exponential lower bounds on fixed-size psd rank and semidefinite extension complexity. arXiv preprint arXiv:1311.2571 (2013)"},{"issue":"2","key":"1795_CR14","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1287\/moor.1120.0575","volume":"38","author":"J Gouveia","year":"2013","unstructured":"Gouveia, J., Parrilo, P.A., Thomas, R.R.: Lifts of convex sets and cone factorizations. Math. Oper. Res. 38(2), 248\u2013264 (2013)","journal-title":"Math. Oper. Res."},{"key":"1795_CR15","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1214\/aos\/1015957395","volume":"28","author":"B Laurent","year":"2000","unstructured":"Laurent, B., Massart, P.: Adaptive estimation of a quadratic functional by model selection. Ann. Stat. 28, 1302\u20131338 (2000)","journal-title":"Ann. Stat."},{"key":"1795_CR16","doi-asserted-by":"crossref","unstructured":"Lee, J.R., Raghavendra, P., Steurer, D.: Lower bounds on the size of semidefinite programming relaxations. In: Proceedings of the forty-seventh annual ACM symposium on theory of computing, pp. 567\u2013576 (2015)","DOI":"10.1145\/2746539.2746599"},{"key":"1795_CR17","unstructured":"O\u2019Donnell, R.: Analysis of Boolean Functions. Cambridge University Press, Cambridge (2014)"},{"key":"1795_CR18","doi-asserted-by":"crossref","unstructured":"O\u2019Rourke, S., Vu, V., Wang, K.: Eigenvectors of random matrices: a survey. J. Comb. Theory Ser. A 144, 361\u2013442 (2016)","DOI":"10.1016\/j.jcta.2016.06.008"},{"key":"1795_CR19","doi-asserted-by":"crossref","unstructured":"Regev, O., Klartag, B.A.: Quantum one-way communication can be exponentially stronger than classical communication. In: Proceedings of the forty-third annual ACM symposium on theory of computing, pp. 31\u201340 (2011)","DOI":"10.1145\/1993636.1993642"},{"key":"1795_CR20","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1795_CR21","volume-title":"High-Dimensional Probability: An Introduction with Applications in Data Science","author":"R Vershynin","year":"2018","unstructured":"Vershynin, R.: High-Dimensional Probability: An Introduction with Applications in Data Science, vol. 47. Cambridge University Press, Cambridge (2018)"},{"issue":"3","key":"1795_CR22","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1016\/0022-0000(91)90024-Y","volume":"43","author":"M Yannakakis","year":"1991","unstructured":"Yannakakis, M.: Expressing combinatorial optimization problems by linear programs. J. Comput. Syst. Sci. 43(3), 441\u2013466 (1991)","journal-title":"J. Comput. Syst. Sci."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-022-01795-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10107-022-01795-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-022-01795-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T22:20:42Z","timestamp":1677018042000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10107-022-01795-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["1795"],"URL":"https:\/\/doi.org\/10.1007\/s10107-022-01795-7","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"type":"print","value":"0025-5610"},{"type":"electronic","value":"1436-4646"}],"subject":[],"published":{"date-parts":[[2022,4,1]]},"assertion":[{"value":"10 May 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}