{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T11:39:58Z","timestamp":1790422798008,"version":"4.1.0"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>We investigate the use of interior-point methods for solving quadratic programming problems with a small number of linear constraints, where the quadratic term consists of a low-rank update to a positive semidefinite matrix. Several formulations of the support vector machine fit into this category. An interesting feature of these particular problems is the volume of data, which can lead to quadratic programs with between 10 and 100 million variables and, if written explicitly, a dense Q matrix. Our code is based on OOQP, an object-oriented interior-point code, with the linear algebra specialized for the support vector machine application. For the targeted massive problems, all of the data is stored out of core and we overlap computation and input\/output to reduce overhead. Results are reported for several linear support vector machine formulations demonstrating that the method is reliable and scalable.<\/jats:p>","DOI":"10.1137\/s1052623400374379","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"783-804","source":"Crossref","is-referenced-by-count":118,"title":["Interior-Point Methods for Massive Support Vector Machines"],"prefix":"10.1137","volume":"13","author":[{"given":"Michael C.","family":"Ferris","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Todd S.","family":"Munson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1080\/10556780008805771"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009715923555"},{"key":"R3","volume-title":"Sampling techniques","author":"Cochran William","year":"1977"},{"key":"R4","first-page":"143","volume":"1","author":"Collobert Ronan","year":"2001","journal-title":"J. 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Ramakrishnan,\n                      A framework for measuring changes in data characteristics\n                      , in Proceedings of the Eighteenth ACM SIGACT\u2010SIGMOD\u2010SIGART Symposium on Principles of Database Systems, May 31\u2013June 2, 1999, Philadelphia, Pennsylvania, ACM Press, New York, 1999, pp. 126\u2013137.","DOI":"10.1145\/303976.303989"},{"key":"R11","unstructured":"M. Gertz and S. Wright,\n                      Object\u2010Oriented Software for Quadratic Programming\n                      , Preprint ANL\/MCS\u2010P891\u20101000, Argonne National Laboratory, Argonne, IL, 2001."},{"key":"R12","unstructured":"M. Gertz and S. Wright,\n                      OOQP User Guide\n                      , Technical Memorandum ANL\/MCS\u2010TM\u2010252, Argonne National Laboratory, Argonne, IL, 2001."},{"key":"R13","volume-title":"Matrix computations","author":"Golub Gene","year":"1996"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00249643"},{"key":"R15","volume-title":"Accuracy and stability of numerical algorithms","author":"Higham Nicholas","year":"1996"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/0471725250"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495293160"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971255"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1113.001.0001"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1109\/72.788643"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1109\/34.877518"},{"key":"R22","unstructured":"O. L. Mangasarian and D. R. Musicant,\n                      Active set support vector machine classification\n                      , in Advances in Neural Information Processing Systems 13, T. K. Leen, T. G. Dietterich, and V. Tresp, eds., MIT Press, Cambridge, MA, 2001, pp. 577\u2013583."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0802028"},{"key":"R24","unstructured":"J. Platt,\n                      Sequential minimal optimization: A fast algorithm for training support vector machines\n                      , in Advances in Kernel Methods\u2014Support Vector Learning, B. Sch\u00f6lkopf, C. J. C. Burges, and A. J. Smola, eds., MIT Press, Cambridge, MA, 1999, pp. 185\u2013208."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0314056"},{"key":"R26","unstructured":"B. Sch\u00f6lkopf, C. Burges, and A. Smola, eds.\n                      Advances in Kernel Methods: Support Vector Machines\n                      , MIT Press, Cambridge, MA, 1998."},{"key":"R27","unstructured":"A. J. Smola,\n                      Learning with Kernels\n                      , Ph.D. thesis, GMD Research Series 25, Technische Universit\u00e4t Berlin, Germany, 1998."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3264-1"},{"key":"R29","volume-title":"The algebraic eigenvalue problem","author":"Wilkinson J.","year":"1965"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971453"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1007\/PL00011431"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623400374379","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:31:09Z","timestamp":1787333469000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623400374379"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S1052623400374379"],"URL":"https:\/\/doi.org\/10.1137\/s1052623400374379","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}