{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T08:02:38Z","timestamp":1751961758129,"version":"3.41.0"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GI-711\/3-1"],"award-info":[{"award-number":["GI-711\/3-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["20PA21-121957"],"award-info":[{"award-number":["20PA21-121957"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p>We consider parameterized convex optimization problems over the unit simplex, that depend on one parameter. We provide a simple and efficient scheme for maintaining an \u03f5-approximate solution (and a corresponding \u03f5-coreset) along the entire parameter path. We prove correctness and optimality of the method. Practically relevant instances of the abstract parameterized optimization problem are for example regularization paths of support vector machines, multiple kernel learning, and minimum enclosing balls of moving points.<\/jats:p>","DOI":"10.1145\/2390176.2390186","type":"journal-article","created":{"date-parts":[[2013,1,2]],"date-time":"2013-01-02T13:23:15Z","timestamp":1357132995000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Approximating parameterized convex optimization problems"],"prefix":"10.1145","volume":"9","author":[{"given":"Joachim","family":"Giesen","sequence":"first","affiliation":[{"name":"Friedrich-Schiller-Universit\u00e4t Jena, Jena, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Jaggi","sequence":"additional","affiliation":[{"name":"ETH Z\u00fcrich, Switzerland, Palaiseau, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00f6ren","family":"Laue","sequence":"additional","affiliation":[{"name":"Friedrich-Schiller-Universit\u00e4t Jena, Jena, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,12,26]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1145\/1008731.1008736"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1145\/1247069.1247135"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1145\/1015330.1015424"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1016\/j.comgeo.2007.04.002"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1145\/1824777.1824783"},{"doi-asserted-by":"publisher","key":"e_1_2_1_6_1","DOI":"10.1214\/07-AOAS131"},{"doi-asserted-by":"publisher","key":"e_1_2_1_7_1","DOI":"10.1145\/1542362.1542370"},{"unstructured":"G\u00e4rtner B. Jaggi M. and Maria C. 2010. An exponential lower bound on the complexity of regularization paths. arXiv.org cs.LG.  G\u00e4rtner B. Jaggi M. and Maria C. 2010. An exponential lower bound on the complexity of regularization paths. arXiv.org cs.LG.","key":"e_1_2_1_8_1"},{"volume-title":"Proceedings of the 18th Annual European Symposium on Algorithms (ESA'10)","author":"Giesen J.","key":"e_1_2_1_9_1"},{"unstructured":"Giesen J. Jaggi M. and Welsch T. 2009. A combinatorial algorithm to compute regularization paths. arXiv.org cs.LG.  Giesen J. Jaggi M. and Welsch T. 2009. A combinatorial algorithm to compute regularization paths. arXiv.org cs.LG.","key":"e_1_2_1_10_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_11_1","DOI":"10.1137\/0304007"},{"doi-asserted-by":"publisher","key":"e_1_2_1_12_1","DOI":"10.5555\/1005332.1044706"},{"unstructured":"Jaggi M. 2011. Sparse convex optimization methods for machine learning. Ph.D. thesis ETH Z\u00fcrich (To appear).  Jaggi M. 2011. Sparse convex optimization methods for machine learning. Ph.D. thesis ETH Z\u00fcrich (To appear).","key":"e_1_2_1_13_1"},{"key":"e_1_2_1_14_1","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"Markowitz H.","year":"1952","journal-title":"J. Finance"},{"unstructured":"Matou\u0161ek J. and G\u00e4rtner B. 2007. Understanding and Using Linear Programming. Springer-Verlag Inc. New York.  Matou\u0161ek J. and G\u00e4rtner B. 2007. Understanding and Using Linear Programming. Springer-Verlag Inc. New York.","key":"e_1_2_1_15_1"},{"doi-asserted-by":"crossref","unstructured":"Mitchell B. Dem'yanov V. and Malozemov V. 1974. Finding the point of a polyhedron closest to the origin. SIAM J. Control.  Mitchell B. Dem'yanov V. and Malozemov V. 1974. Finding the point of a polyhedron closest to the origin. SIAM J. Control.","key":"e_1_2_1_16_1","DOI":"10.1137\/0312003"},{"key":"e_1_2_1_17_1","first-page":"2491","article-title":"SimpleMKL","volume":"9","author":"Rakotomamonjy A.","year":"2008","journal-title":"J. Mach. Learn. Res."},{"doi-asserted-by":"publisher","key":"e_1_2_1_18_1","DOI":"10.1214\/009053606000001370"},{"doi-asserted-by":"publisher","key":"e_1_2_1_19_1","DOI":"10.5555\/1046920.1058114"},{"volume-title":"Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. DMMT Workshop.","author":"Wu Z.","key":"e_1_2_1_20_1"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2390176.2390186","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2390176.2390186","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:35:45Z","timestamp":1750235745000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2390176.2390186"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1145\/2390176.2390186"],"URL":"https:\/\/doi.org\/10.1145\/2390176.2390186","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2012,12]]},"assertion":[{"value":"2010-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-10-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-12-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}