{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T09:00:58Z","timestamp":1787389258759,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,11]]},"abstract":"<jats:p>A primal-dual infeasible-interior-point path-following algorithm is proposed for solving semidefinite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible, the algorithm finds an optimal solution in at most $O(\\sqrt{n}L)$ iterations, where n is the size of the problem and L is the logarithm of the ratio of the initial error and the tolerance. If the starting point is large enough, then the algorithm terminates in at most O(nL) steps either by finding a solution or by determining that the primal-dual problem has no solution of norm less than a given number. Moreover, we propose a sufficient condition for the superlinear convergence of the algorithm. In addition, we give two special cases of SDP for which the algorithm is quadratically convergent.<\/jats:p>","DOI":"10.1137\/s1052623495294955","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1007-1028","source":"Crossref","is-referenced-by-count":64,"title":["A Superlinearly Convergent Primal-Dual Infeasible-Interior-Point Algorithm for Semidefinite Programming"],"prefix":"10.1137","volume":"8","author":[{"given":"Florian A.","family":"Potra","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rongqin","family":"Sheng","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":"10.1016\/S0025-5610(96)00079-2"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0806020"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"R. A. Horn and C. R. Johnson,\n                      Matrix Analysis\n                      , Cambridge University Press, New York, 1985.","DOI":"10.1017\/CBO9780511810817"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02192304"},{"key":"R7","first-page":"1","author":"Kojima Masakazu","year":"1997","journal-title":"S\u016brikaisekikenky\u016bsho K\u014dky\u016broku"},{"key":"R8","unstructured":"M. Kojima, M. Shida, and S. Shindoh,\n                      Global and Local Convergence of Predictor\u2010Corrector Infeasible\u2010Interior\u2010Point Algorithms for Semidefinite Programs\n                      , Research Reports on Information Sciences B\u2010305, Department of Information Sciences, Tokyo Institute of Technology, 2\u201012\u20101 Oh\u2010Okayama, Meguro\u2010ku, Tokyo 152, Japan, 1995."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494269035"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/s002459900016"},{"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":"10.1137\/S1052623495290209"},{"key":"R14","unstructured":"M. L. Overton,\n                      private communication\n                      ."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623494267826"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1137\/1038003"},{"key":"R17","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\/S1052623495294955","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:55:10Z","timestamp":1787331310000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623495294955"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,11]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.1137\/S1052623495294955"],"URL":"https:\/\/doi.org\/10.1137\/s1052623495294955","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,11]]}}}