{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T22:11:24Z","timestamp":1717625484732},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2014,12,14]],"date-time":"2014-12-14T00:00:00Z","timestamp":1418515200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s10107-014-0852-3","type":"journal-article","created":{"date-parts":[[2014,12,13]],"date-time":"2014-12-13T07:24:27Z","timestamp":1418455467000},"page":"403-433","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Conic version of Loewner\u2013John ellipsoid theorem"],"prefix":"10.1007","volume":"155","author":[{"given":"Alberto","family":"Seeger","sequence":"first","affiliation":[]},{"given":"Mounir","family":"Torki","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,12,14]]},"reference":[{"key":"852_CR1","unstructured":"Ball., K.: An elementary introduction to modern convex geometry. In: Levy, S. (ed.) Flavors of Geometry. Mathematical Sciences Research Institute Publications, vol. 31, pp. 1\u201358. Cambridge University Press, Cambridge (1997)"},{"key":"852_CR2","volume-title":"Nonnegative Matrices in Dynamic Systems","author":"A Berman","year":"1989","unstructured":"Berman, A., Neumann, M., Stern, R.J.: Nonnegative Matrices in Dynamic Systems. Wiley, New York (1989)"},{"key":"852_CR3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TSMCA.2002.1021114","volume":"32","author":"GC Calafiore","year":"2002","unstructured":"Calafiore, G.C.: Approximation of n-dimensional data using spherical and ellipsoidal primitives. IEEE Trans. Syst. Man Cybern. 32, 269\u2013278 (2002)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"852_CR4","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0362-546X(85)90049-5","volume":"9","author":"R Correa","year":"1985","unstructured":"Correa, R., Seeger, A.: Directional derivative of a minimax function. Nonlinear Anal. 9, 13\u201322 (1985)","journal-title":"Nonlinear Anal."},{"key":"852_CR5","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1137\/0114053","volume":"14","author":"JM Danskin","year":"1966","unstructured":"Danskin, J.M.: The theory of max\u2013min, with applications. SIAM J. Appl. Math. 14, 641\u2013664 (1966)","journal-title":"SIAM J. Appl. Math."},{"key":"852_CR6","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 University Press, New York (1994)"},{"key":"852_CR7","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1090\/S0025-5718-1964-0166905-0","volume":"18","author":"DD Fisher","year":"1964","unstructured":"Fisher, D.D.: Minimum ellipsoids. Math. Comput. 18, 669\u2013673 (1964)","journal-title":"Math. Comput."},{"key":"852_CR8","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1287\/moor.5.3.388","volume":"5","author":"J-L Goffin","year":"1980","unstructured":"Goffin, J.-L.: The relaxation method for solving systems of linear inequalities. Math. Oper. Res. 5, 388\u2013414 (1980)","journal-title":"Math. Oper. Res."},{"key":"852_CR9","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1590\/S1807-03022010000200007","volume":"29","author":"D Gourion","year":"2010","unstructured":"Gourion, D., Seeger, A.: Deterministic and stochastic methods for computing volumetric moduli of convex cones. Comput. Appl. Math. 29, 215\u2013246 (2010)","journal-title":"Comput. Appl. Math."},{"key":"852_CR10","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1007\/s11117-011-0140-x","volume":"16","author":"D Gourion","year":"2012","unstructured":"Gourion, D., Seeger, A.: Solidity indices for convex cones. Positivity 16, 685\u2013705 (2012)","journal-title":"Positivity"},{"key":"852_CR11","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1287\/moor.21.4.860","volume":"21","author":"O G\u00fcler","year":"1996","unstructured":"G\u00fcler, O.: Barrier functions in interior point methods. Math. Oper. Res. 21, 860\u2013885 (1996)","journal-title":"Math. Oper. Res."},{"key":"852_CR12","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1080\/10556788.2011.626037","volume":"27","author":"O G\u00fcler","year":"2012","unstructured":"G\u00fcler, O., G\u00fcrtuna, F.: Symmetry of convex sets and its applications to the extremal ellipsoids of convex bodies. Optim. Methods Softw. 27, 735\u2013759 (2012)","journal-title":"Optim. Methods Softw."},{"key":"852_CR13","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1007\/s00454-011-9354-8","volume":"46","author":"PM Gruber","year":"2011","unstructured":"Gruber, P.M.: John and Loewner ellipsoids. Discrete Comput. Geom. 46, 776\u2013788 (2011)","journal-title":"Discrete Comput. Geom."},{"key":"852_CR14","doi-asserted-by":"crossref","unstructured":"Henk, M.: L\u00f6wner\u2013John ellipsoids. Doc. Math. Extra Vol. Optim. Stor., 95\u2013106 (2012)","DOI":"10.4171\/dms\/6\/15"},{"key":"852_CR15","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s11228-009-0131-2","volume":"18","author":"R Henrion","year":"2010","unstructured":"Henrion, R., Seeger, A.: On properties of different notions of centers for convex cones. Set-Valued Var. Anal. 18, 205\u2013231 (2010)","journal-title":"Set-Valued Var. Anal."},{"key":"852_CR16","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s11228-010-0150-z","volume":"18","author":"R Henrion","year":"2010","unstructured":"Henrion, R., Seeger, A.: Inradius and circumradius of various convex cones arising in applications. Set-Valued Var. Anal. 18, 483\u2013511 (2010)","journal-title":"Set-Valued Var. Anal."},{"key":"852_CR17","first-page":"267","volume":"11","author":"A Iusem","year":"2004","unstructured":"Iusem, A., Seeger, A.: Pointedness, connectedness, and convergence results in the space of closed convex cones. J. Convex Anal. 11, 267\u2013284 (2004)","journal-title":"J. Convex Anal."},{"key":"852_CR18","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1590\/S0101-82052005000200006","volume":"24","author":"A Iusem","year":"2005","unstructured":"Iusem, A., Seeger, A.: Axiomatization of the index of pointedness for closed convex cones. Comput. Appl. Math. 24, 245\u2013283 (2005)","journal-title":"Comput. Appl. Math."},{"key":"852_CR19","first-page":"1033","volume":"17","author":"A Iusem","year":"2010","unstructured":"Iusem, A., Seeger, A.: Distances between closed convex cones: old and new results. J. Convex Anal. 17, 1033\u20131055 (2010)","journal-title":"J. Convex Anal."},{"key":"852_CR20","volume-title":"Extremum Problems with Inequalities as Subsidiary Conditions. Studies and Essays Presented to R. Courant on his 60th Birthday","author":"F John","year":"1948","unstructured":"John, F.: Extremum Problems with Inequalities as Subsidiary Conditions. Studies and Essays Presented to R. Courant on his 60th Birthday. Interscience Publ, New York (1948)"},{"key":"852_CR21","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF01582265","volume":"48","author":"LM Kelly","year":"1990","unstructured":"Kelly, L.M., Murty, K.G., Watson, L.T.: CP-rays in simplicial cones. Math. Program. 48, 387\u2013414 (1990)","journal-title":"Math. Program."},{"key":"852_CR22","doi-asserted-by":"crossref","unstructured":"Lasserre., J.B.: A generalization of L\u00f6wner\u2013John\u2019s ellipsoid theorem. Math. Program. Ser. A (2014). doi: 10.1007\/s10107-014-0798-5","DOI":"10.1007\/s10107-014-0798-5"},{"key":"852_CR23","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970791","volume-title":"Interior-Point Polynomial Algorithms in Convex Programming","author":"Y Nesterov","year":"1994","unstructured":"Nesterov, Y., Nemirovskii, A.S.: Interior-Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied Mathematics, Philadelphia, PA (1994)"},{"key":"852_CR24","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1007\/s13366-013-0171-5","volume":"55","author":"A Seeger","year":"2014","unstructured":"Seeger, A., Torki, M.: On highly eccentric cones. Beitr. Algebra Geom. 55, 521\u2013544 (2014)","journal-title":"Beitr. Algebra Geom."},{"key":"852_CR25","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1007\/s11750-013-0289-5","volume":"22","author":"A Seeger","year":"2014","unstructured":"Seeger, A., Torki, M.: Centers of sets with symmetry or cyclicity properties. TOP 22, 716\u2013738 (2014)","journal-title":"TOP"},{"key":"852_CR26","doi-asserted-by":"crossref","unstructured":"Seeger., A, Torki., M.: Centers and partial volumes of convex cones. I. Basic theory. Beitr. Algebra Geom. online since (Sept 2014)","DOI":"10.1007\/s13366-014-0220-8"},{"key":"852_CR27","doi-asserted-by":"crossref","unstructured":"Seeger., A, Torki., M.: Centers and partial volumes of convex cones. II. Advanced topics. Beitr. Algebra Geom., online since (Sept 2014)","DOI":"10.1007\/s13366-014-0221-7"},{"key":"852_CR28","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.aml.2012.10.014","volume":"26","author":"S Sitarz","year":"2013","unstructured":"Sitarz, S.: The medal points\u2019 incenter for rankings in sport. Appl. Math. Lett. 26, 408\u2013412 (2013)","journal-title":"Appl. Math. Lett."},{"key":"852_CR29","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0024-3795(91)90161-O","volume":"150","author":"R Stern","year":"1991","unstructured":"Stern, R., Wolkowicz, H.: Invariant ellipsoidal cones. Linear Algebra Appl. 150, 81\u2013106 (1991)","journal-title":"Linear Algebra Appl."},{"key":"852_CR30","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1137\/0612012","volume":"12","author":"R Stern","year":"1991","unstructured":"Stern, R., Wolkowicz, H.: Exponential nonnegativity on the ice cream cone. SIAM J. Matrix Anal. Appl. 12, 160\u2013165 (1991)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"852_CR31","first-page":"340","volume":"12","author":"EB Vinberg","year":"1963","unstructured":"Vinberg, E.B.: The theory of convex homogeneous cones. Trans. Moskow Math. 12, 340\u2013403 (1963)","journal-title":"Trans. Moskow Math."},{"key":"852_CR32","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1090\/S0002-9939-1967-0209806-6","volume":"18","author":"DW Walkup","year":"1967","unstructured":"Walkup, D.W., Wets, R.J.B.: Continuity of some convex-cone-valued mappings. Proc. Am. Math. Soc. 18, 229\u2013235 (1967)","journal-title":"Proc. Am. Math. Soc."},{"key":"852_CR33","first-page":"263","volume":"51","author":"MJ Weber","year":"2010","unstructured":"Weber, M.J., Schr\u00f6cker, H.P.: Davis\u2019 convexity theorem and extremal ellipsoids. Beitr. Algebra Geom. 51, 263\u2013274 (2010)","journal-title":"Beitr. Algebra Geom."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-014-0852-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-014-0852-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-014-0852-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T21:39:40Z","timestamp":1717623580000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-014-0852-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,14]]},"references-count":33,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["852"],"URL":"https:\/\/doi.org\/10.1007\/s10107-014-0852-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,14]]}}}