{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T16:43:56Z","timestamp":1781887436750,"version":"3.54.5"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18H03206"],"award-info":[{"award-number":["18H03206"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["19K20217"],"award-info":[{"award-number":["19K20217"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s10107-019-01439-3","type":"journal-article","created":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T09:04:32Z","timestamp":1573117472000},"page":"1-48","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Amenable cones: error bounds without constraint qualifications"],"prefix":"10.1007","volume":"186","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2369-0107","authenticated-orcid":false,"given":"Bruno F.","family":"Louren\u00e7o","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,11,7]]},"reference":[{"issue":"1","key":"1439_CR1","first-page":"161","volume":"14","author":"N Arima","year":"2018","unstructured":"Arima, N., Kim, S., Kojima, M., Toh, K.-C.: Lagrangian-conic relaxations, part I: a unified framework and its applications to quadratic optimization problems. Pac. J. Optim. 14(1), 161\u2013192 (2018)","journal-title":"Pac. J. Optim."},{"issue":"3","key":"1439_CR2","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10589-016-9879-0","volume":"66","author":"N Arima","year":"2017","unstructured":"Arima, N., Kim, S., Kojima, M., Toh, K.-C.: A robust Lagrangian-DNN method for a class of quadratic optimization problems. Comput. Optim. Appl. 66(3), 453\u2013479 (2017)","journal-title":"Comput. Optim. Appl."},{"issue":"11","key":"1439_CR3","doi-asserted-by":"crossref","first-page":"2395","DOI":"10.1080\/02331934.2014.979323","volume":"64","author":"M Baes","year":"2015","unstructured":"Baes, M., Lin, H.: A Lipschitzian error bound for monotone symmetric cone linear complementarity problem. Optimization 64(11), 2395\u20132416 (2015)","journal-title":"Optimization"},{"key":"1439_CR4","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0024-3795(78)90072-1","volume":"22","author":"GP Barker","year":"1978","unstructured":"Barker, G.P.: Perfect cones. Linear Algebra Appl. 22, 211\u2013221 (1978)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"1439_CR5","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s101070050083","volume":"86","author":"HH Bauschke","year":"1999","unstructured":"Bauschke, H.H., Borwein, J.M., Li, W.: Strong conical hull intersection property, bounded linear regularity, Jameson\u2019s property (G), and error bounds in convex optimization. Math. Program. 86(1), 135\u2013160 (1999)","journal-title":"Math. Program."},{"issue":"03","key":"1439_CR6","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1017\/S1446788700017250","volume":"30","author":"JM Borwein","year":"1981","unstructured":"Borwein, J.M., Wolkowicz, H.: Facial reduction for a cone-convex programming problem. J. Aust. Math. Soc. (Ser. A) 30(03), 369\u2013380 (1981)","journal-title":"J. Aust. Math. Soc. (Ser. A)"},{"issue":"2","key":"1439_CR7","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1016\/0022-247X(81)90138-4","volume":"83","author":"JM Borwein","year":"1981","unstructured":"Borwein, J.M., Wolkowicz, H.: Regularizing the abstract convex program. J. Math. Anal. Appl. 83(2), 495\u2013530 (1981)","journal-title":"J. Math. Anal. Appl."},{"key":"1439_CR8","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BFb0120983","volume-title":"Optimality and Stability in Mathematical Programming","author":"JM Borwein","year":"1982","unstructured":"Borwein, J.M., Wolkowicz, H.: Characterizations of optimality without constraint qualification for the abstract convex program. In: Guignard, M. (ed.) Optimality and Stability in Mathematical Programming, pp. 77\u2013100. Springer, Berlin (1982)"},{"key":"1439_CR9","series-title":"Springer Proceedings in Mathematics and Statistics","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/978-1-4614-7621-4_12","volume-title":"Computational and Analytical Mathematics","author":"Y-L Cheung","year":"2013","unstructured":"Cheung, Y.-L., Schurr, S., Wolkowicz, H.: Preprocessing and regularization for degenerate semidefinite programs. In: Bailey, D.H., Bauschke, H.H., Borwein, P., Garvan, F., Th\u00e9ra, M., Vanderwerff, J.D., Wolkowicz, H. (eds.) Computational and Analytical Mathematics. Springer Proceedings in Mathematics and Statistics, vol. 50, pp. 251\u2013303. Springer, New York (2013)"},{"issue":"2","key":"1439_CR10","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1137\/S1052623402406765","volume":"14","author":"CB Chua","year":"2003","unstructured":"Chua, C.B.: Relating homogeneous cones and positive definite cones via T-algebras. SIAM J. Optim. 14(2), 500\u2013506 (2003)","journal-title":"SIAM J. Optim."},{"key":"1439_CR11","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s10107-006-0072-6","volume":"111","author":"CB Chua","year":"2008","unstructured":"Chua, C.B., Tun\u00e7el, L.: Invariance and efficiency of convex representations. Math. Program. 111, 113\u2013140 (2008)","journal-title":"Math. Program."},{"issue":"1","key":"1439_CR12","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10107-016-1048-9","volume":"162","author":"D Drusvyatskiy","year":"2017","unstructured":"Drusvyatskiy, D., Li, G., Wolkowicz, H.: A note on alternating projections for ill-posed semidefinite feasibility problems. Math. Program. 162(1), 537\u2013548 (2017)","journal-title":"Math. Program."},{"issue":"2","key":"1439_CR13","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1137\/140968318","volume":"25","author":"D Drusvyatskiy","year":"2015","unstructured":"Drusvyatskiy, D., Pataki, G., Wolkowicz, H.: Coordinate shadows of semidefinite and euclidean distance matrices. SIAM J. Optim. 25(2), 1160\u20131178 (2015)","journal-title":"SIAM J. Optim."},{"key":"1439_CR14","doi-asserted-by":"crossref","unstructured":"Drusvyatskiy, D., Wolkowicz, H.: The many faces of degeneracy in conic optimization. Technical report, University of Washington (2017)","DOI":"10.1561\/9781680833911"},{"key":"1439_CR15","series-title":"Oxford Mathematical Monographs","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198534778.001.0001","volume-title":"Analysis on Symmetric Cones","author":"J Faraut","year":"1994","unstructured":"Faraut, J., Kor\u00e1nyi, A.: Analysis on Symmetric Cones. Oxford Mathematical Monographs. Clarendon Press, Oxford (1994)"},{"issue":"2","key":"1439_CR16","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1023\/A:1020643711475","volume":"74","author":"L Faybusovich","year":"2002","unstructured":"Faybusovich, L.: On Nesterov\u2019s approach to semi-infinite programming. Acta Appl. Math. 74(2), 195\u2013215 (2002)","journal-title":"Acta Appl. Math."},{"issue":"2","key":"1439_CR17","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1137\/050635560","volume":"17","author":"L Faybusovich","year":"2006","unstructured":"Faybusovich, L.: Jordan-algebraic approach to convexity theorems for quadratic mappings. SIAM J. Optim. 17(2), 558\u2013576 (2006)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1439_CR18","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1080\/02331930701523510","volume":"57","author":"L Faybusovich","year":"2008","unstructured":"Faybusovich, L.: Several Jordan-algebraic aspects of optimization. Optimization 57(3), 379\u2013393 (2008)","journal-title":"Optimization"},{"issue":"6","key":"1439_CR19","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/j.orl.2016.08.004","volume":"44","author":"HA Friberg","year":"2016","unstructured":"Friberg, H.A.: A relaxed-certificate facial reduction algorithm based on subspace intersection. Oper. Res. Lett. 44(6), 718\u2013722 (2016)","journal-title":"Oper. Res. Lett."},{"issue":"6","key":"1439_CR20","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1016\/j.laa.2009.11.015","volume":"432","author":"MS Gowda","year":"2010","unstructured":"Gowda, M.S., Sznajder, R.: Schur complements, Schur determinantal and Haynsworth inertia formulas in Euclidean Jordan algebras. Linear Algebra Appl. 432(6), 1553\u20131559 (2010)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"1439_CR21","doi-asserted-by":"crossref","first-page":"263","DOI":"10.6028\/jres.049.027","volume":"49","author":"AJ Hoffman","year":"1957","unstructured":"Hoffman, A.J.: On approximate solutions of systems of linear inequalities. J. Res. Natl. Bur. Stand. 49(4), 263\u2013265 (1957)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"1439_CR22","series-title":"Springer Monographs in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-64277-2","volume-title":"Variational Analysis of Regular Mappings: Theory and Applications","author":"AD Ioffe","year":"2017","unstructured":"Ioffe, A.D.: Variational Analysis of Regular Mappings: Theory and Applications. Springer Monographs in Mathematics. Springer, Berlin (2017)"},{"key":"1439_CR23","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.laa.2017.06.043","volume":"532","author":"M Ito","year":"2017","unstructured":"Ito, M., Louren\u00e7o, B.F.: A bound on the Carath\u00e9odory number. Linear Algebra Appl. 532, 347\u2013363 (2017)","journal-title":"Linear Algebra Appl."},{"key":"1439_CR24","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.laa.2017.07.029","volume":"533","author":"M Ito","year":"2017","unstructured":"Ito, M., Louren\u00e7o, B.F.: The $$p$$-cones in dimension $$n\\ge 3$$ are not homogeneous when $$p\\ne 2$$. Linear Algebra Appl. 533, 326\u2013335 (2017)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"1439_CR25","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.jmaa.2018.10.081","volume":"471","author":"M Ito","year":"2019","unstructured":"Ito, M., Louren\u00e7o, B.F.: The automorphism group and the non-self-duality of p-cones. J. Math. Anal. Appl. 471(1), 392\u2013410 (2019)","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"1439_CR26","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/s10107-015-0874-5","volume":"156","author":"S Kim","year":"2016","unstructured":"Kim, S., Kojima, M., Toh, K.-C.: A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. Math. Program. 156(1), 161\u2013187 (2016)","journal-title":"Math. Program."},{"key":"1439_CR27","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0096285","volume-title":"The Minnesota Notes on Jordan Algebras and Their Applications","author":"M Koecher","year":"1999","unstructured":"Koecher, M.: The Minnesota Notes on Jordan Algebras and Their Applications. Lecture Notes in Mathematics, vol. 1710. Springer, Berlin (1999)"},{"key":"1439_CR28","series-title":"Generalized Monotonicity: Recent Results","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/978-1-4613-3341-8_3","volume-title":"Generalized Convexity","author":"AS Lewis","year":"1998","unstructured":"Lewis, A.S., Pang, J.-S.: Error bounds for convex inequality systems. In: Crouzeix, J.-P., Mart\u00ednez-Legaz, J.-E., Volle, M. (eds.) Generalized Convexity. Generalized Monotonicity: Recent Results, pp. 75\u2013110. Springer, New York (1998)"},{"issue":"2","key":"1439_CR29","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1007\/s10107-017-1136-5","volume":"167","author":"M Liu","year":"2018","unstructured":"Liu, M., Pataki, G.: Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming. Math. Program. 167(2), 435\u2013480 (2018)","journal-title":"Math. Program."},{"key":"1439_CR30","unstructured":"Louren\u00e7o, B.F., Muramatsu, M., Tsuchiya, T.: Solving SDP completely with an interior point oracle. arXiv e-prints arXiv:1507.08065 (2015)"},{"issue":"3","key":"1439_CR31","doi-asserted-by":"crossref","first-page":"2304","DOI":"10.1137\/15M1051634","volume":"28","author":"BF Louren\u00e7o","year":"2018","unstructured":"Louren\u00e7o, B.F., Muramatsu, M., Tsuchiya, T.: Facial reduction and partial polyhedrality. SIAM J. Optim. 28(3), 2304\u20132326 (2018)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1439_CR32","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.1287\/moor.2017.0901","volume":"43","author":"BF Louren\u00e7o","year":"2018","unstructured":"Louren\u00e7o, B.F., Fukuda, E.H., Fukushima, M.: Optimality conditions for problems over symmetric cones and a simple augmented Lagrangian method. Math. Oper. Res. 43(4), 1233\u20131251 (2018)","journal-title":"Math. Oper. Res."},{"key":"1439_CR33","volume-title":"Handbook of Semidefinite Programming: Theory, Algorithms, and Applications","author":"Z Luo","year":"2000","unstructured":"Luo, Z., Sturm, J.F.: Error analysis. In: Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.) Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"1439_CR34","unstructured":"Luo, Z., Sturm, J.F., Zhang, S.: Duality results for conic convex programming. Technical report, Econometric Institute, Erasmus University Rotterdam, The Netherlands (1997)"},{"issue":"1","key":"1439_CR35","first-page":"299","volume":"79","author":"J-S Pang","year":"1997","unstructured":"Pang, J.-S.: Error bounds in mathematical programming. Math. Program. 79(1), 299\u2013332 (1997)","journal-title":"Math. Program."},{"key":"1439_CR36","volume-title":"Handbook of Semidefinite Programming: Theory, Algorithms, and Applications","author":"G Pataki","year":"2000","unstructured":"Pataki, G.: The geometry of semidefinite programming. In: Wolkowicz, H., Saigal, R., Vandenberghe, L. (eds.) Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. Kluwer Academic Publishers, Dordrecht (2000)"},{"issue":"1","key":"1439_CR37","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jmaa.2012.10.033","volume":"400","author":"G Pataki","year":"2013","unstructured":"Pataki, G.: On the connection of facially exposed and nice cones. J. Math. Anal. Appl. 400(1), 211\u2013221 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"1439_CR38","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/978-1-4614-7621-4_28","volume-title":"Computational and Analytical Mathematics","author":"G Pataki","year":"2013","unstructured":"Pataki, G.: Strong duality in conic linear programming: facial reduction and extended duals. In: Bailey, D.H., Bauschke, H.H., Borwein, P., Garvan, F., Th\u00e9ra, M., Vanderwerff, J.D., Wolkowicz, H. (eds.) Computational and Analytical Mathematics, vol. 50, pp. 613\u2013634. Springer, New York (2013)"},{"key":"1439_CR39","unstructured":"Permenter, F.: Private Communication (2016)"},{"issue":"3","key":"1439_CR40","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1137\/15M1049415","volume":"27","author":"F Permenter","year":"2017","unstructured":"Permenter, F., Friberg, H.A., Andersen, E.D.: Solving conic optimization problems via self-dual embedding and facial reduction: a unified approach. SIAM J. Optim. 27(3), 1257\u20131282 (2017)","journal-title":"SIAM J. Optim."},{"key":"1439_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10107-017-1169-9","volume":"171","author":"F Permenter","year":"2017","unstructured":"Permenter, F., Parrilo, P.: Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone. Math. Program. 171, 1\u201354 (2017)","journal-title":"Math. Program."},{"key":"1439_CR42","unstructured":"P\u00f3lik, I., Terlaky, T.: Exact duality for optimization over symmetric cones. AdvOL Report 2007\/10, McMaster University, Advanced Optimization Lab, Hamilton, Canada. http:\/\/www.optimization-online.org\/DB_HTML\/2007\/08\/1754.html (2007)"},{"issue":"4","key":"1439_CR43","doi-asserted-by":"crossref","first-page":"2649","DOI":"10.1137\/15M1027371","volume":"26","author":"J Renegar","year":"2016","unstructured":"Renegar, J.: \u201cEfficient\u201d subgradient methods for general convex optimization. SIAM J. Optim. 26(4), 2649\u20132676 (2016)","journal-title":"SIAM J. Optim."},{"key":"1439_CR44","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"issue":"1","key":"1439_CR45","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1137\/130922069","volume":"24","author":"V Roshchina","year":"2014","unstructured":"Roshchina, V.: Facially exposed cones are not always nice. SIAM J. Optim. 24(1), 257\u2013268 (2014)","journal-title":"SIAM J. Optim."},{"issue":"3","key":"1439_CR46","doi-asserted-by":"publisher","first-page":"2363","DOI":"10.1137\/17M1126643","volume":"29","author":"V Roshchina","year":"2019","unstructured":"Roshchina, V., Tun\u00e7el, L.: Facially dual complete (nice) cones and lexicographic tangents. SIAM J. Optim. 29(3), 2363\u20132387 (2019). https:\/\/doi.org\/10.1137\/17M1126643","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1439_CR47","doi-asserted-by":"crossref","first-page":"1228","DOI":"10.1137\/S1052623498338606","volume":"10","author":"JF Sturm","year":"2000","unstructured":"Sturm, J.F.: Error bounds for linear matrix inequalities. SIAM J. Optim. 10(4), 1228\u20131248 (2000)","journal-title":"SIAM J. Optim."},{"issue":"1\u20133","key":"1439_CR48","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0024-3795(00)00096-3","volume":"312","author":"JF Sturm","year":"2000","unstructured":"Sturm, J.F.: Similarity and other spectral relations for symmetric cones. Linear Algebra Appl. 312(1\u20133), 135\u2013154 (2000)","journal-title":"Linear Algebra Appl."},{"key":"1439_CR49","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0024-3795(90)90401-W","volume":"139","author":"C-H Sung","year":"1990","unstructured":"Sung, C.-H., Tam, B.-S.: A study of projectionally exposed cones. Linear Algebra Appl. 139, 225\u2013252 (1990)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"1439_CR50","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1017\/S1446788700016311","volume":"22","author":"B-S Tam","year":"1976","unstructured":"Tam, B.-S.: A note on polyhedral cones. J. Aust. Math. Soc. 22(4), 456\u2013461 (1976)","journal-title":"J. Aust. Math. Soc."},{"issue":"2","key":"1439_CR51","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s10589-012-9480-0","volume":"53","author":"L Tun\u00e7el","year":"2012","unstructured":"Tun\u00e7el, L., Wolkowicz, H.: Strong duality and minimal representations for cone optimization. Comput. Optim. Appl. 53(2), 619\u2013648 (2012)","journal-title":"Comput. Optim. Appl."},{"issue":"1","key":"1439_CR52","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/s10957-012-0219-y","volume":"158","author":"H Waki","year":"2013","unstructured":"Waki, H., Muramatsu, M.: Facial reduction algorithms for conic optimization problems. J. Optim. Theory Appl. 158(1), 188\u2013215 (2013)","journal-title":"J. Optim. Theory Appl."},{"key":"1439_CR53","unstructured":"Yamashita, H.: Error bounds for nonlinear semidefinite optimization. Optimization Online (2016). http:\/\/www.optimization-online.org\/DB_HTML\/2016\/10\/5682.html"},{"key":"1439_CR54","doi-asserted-by":"publisher","unstructured":"Yoshise, A., Matsukawa, Y.: On optimization over the doubly nonnegative cone. In: IEEE International Symposium on Computer-Aided Control System Design (CACSD), pp 13\u201318 (2010). https:\/\/doi.org\/10.1109\/CACSD.2010.5612811","DOI":"10.1109\/CACSD.2010.5612811"},{"issue":"3","key":"1439_CR55","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s12532-019-00164-4","volume":"11","author":"Y Zhu","year":"2019","unstructured":"Zhu, Y., Pataki, G., Tran-Dinh, Q.: Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs. Math. Program. Comput. 11(3), 503\u2013586 (2019)","journal-title":"Math. Program. Comput."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01439-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-019-01439-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-019-01439-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T11:31:38Z","timestamp":1721993498000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-019-01439-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,7]]},"references-count":55,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["1439"],"URL":"https:\/\/doi.org\/10.1007\/s10107-019-01439-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,7]]},"assertion":[{"value":"17 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 September 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}