{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T20:40:23Z","timestamp":1791837623990,"version":"4.3.4"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,2]]},"abstract":"<jats:p>\n                    This paper establishes the superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming (SDP) under the assumptions that the semidefinite program has a strictly complementary primal-dual optimal solution and that the size of the central path neighborhood tends to zero. The interior point algorithm considered here closely resembles the Mizuno--Todd--Ye predictor-corrector method for linear programming which is known to be quadratically convergent. It is shown that when the iterates are well centered, the duality gap is reduced superlinearly after each predictor step. Indeed, if each predictor step is succeeded by r consecutive corrector steps then the predictor reduces the duality gap superlinearly with order 2 ( 1 + 2\n                    <jats:sup>- r<\/jats:sup>\n                    ). The proof relies on a careful analysis of the central path for SDP. It is shown that under the strict complementarity assumption, the primal-dual central path converges to the analytic center of the primal-dual optimal solution set, and the distance from any point on the central path to this analytic center is bounded by the duality gap.\n                  <\/jats:p>","DOI":"10.1137\/s1052623496299187","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"59-81","source":"Crossref","is-referenced-by-count":65,"title":["Superlinear Convergence of a Symmetric Primal-Dual Path Following Algorithm for Semidefinite Programming"],"prefix":"10.1137","volume":"8","author":[{"given":"Zhi-Quan","family":"Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos F.","family":"Sturm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuzhong","family":"Zhang","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\/0805002"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496304700"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581702"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0806020"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.6028\/jres.049.027"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-54509-3"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1007\/BF01581723"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494269035"},{"key":"R9","unstructured":"C. J. Lin and R. Saigal,\n                      An Infeasible Start Predictor Corrector Method for Semi\u2010Definite Linear Programming\n                      , Tech. report, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 1995."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"N. Megiddo,\n                      Pathways to the optimal solution set in linear programming\n                      , in Progress in Mathematical Programming, Interior\u2010Point and Related Methods, N. Megiddo, ed., Springer\u2010Verlag, New York, 1989, pp. 131\u2013158.","DOI":"10.1007\/978-1-4613-9617-8_8"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1287\/moor.18.4.964"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495293056"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1287\/moor.21.4.793"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1287\/moor.22.1.1"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495290209"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495294955"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Jos Sturm, Shuzhong Zhang, Symmetric primal\u2010dual path\u2010following algorithms for semidefinite programming, Proceedings of the Stieltjes Workshop on High Performance Optimization Techniques (HPOPT \u201996) (Delft), Vol. 29, 1999, 301\u201331599m:90110","DOI":"10.1016\/S0168-9274(98)00099-3"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5610(94)00062-X"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/1038003"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01585182"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495296115"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1052623496299187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:00:41Z","timestamp":1787331641000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623496299187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1998,2]]}},"alternative-id":["10.1137\/S1052623496299187"],"URL":"https:\/\/doi.org\/10.1137\/s1052623496299187","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,2]]}}}