{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:31Z","timestamp":1787333671424,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,5]]},"abstract":"<jats:p>In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see Yu. E. Nesterov and M.J. Todd, Math. Oper. Res., 22 (1997), pp. 1--42). The class of problems under consideration includes linear programming, semidefinite programming, and convex quadratically constrained, quadratic programming problems. For such problems we introduce a new definition of affine-scaling and centering directions. We present efficiency estimates for several symmetric primal-dual methods that can loosely be classified as path-following methods. Because of the special properties of these cones and barriers, two of our algorithms can take steps that typically go a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.<\/jats:p>","DOI":"10.1137\/s1052623495290209","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"324-364","source":"Crossref","is-referenced-by-count":368,"title":["Primal-Dual Interior-Point Methods for Self-Scaled Cones"],"prefix":"10.1137","volume":"8","author":[{"given":"Yu. E.","family":"Nesterov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. J.","family":"Todd","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971088"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.21.4.860"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579150"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587074"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1287\/moor.18.4.964"},{"key":"R6","first-page":"75","volume":"32","author":"Mizuno Shinji","year":"1989","journal-title":"J. Oper. Res. Soc. Japan"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01587075"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00034-2"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"Yu. Nesterov and A. Nemirovskii,\n                      Interior Point Polynomial Algorithms in Convex Programming\n                      , SIAM, Philadelphia, 1994.","DOI":"10.1137\/1.9781611970791"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1287\/moor.22.1.1"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02942030"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S105262349630060X"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623495290209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:16:53Z","timestamp":1787332613000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623495290209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,5]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,5]]}},"alternative-id":["10.1137\/S1052623495290209"],"URL":"https:\/\/doi.org\/10.1137\/s1052623495290209","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,5]]}}}