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This last observation also leads to convenient computation of accelerated steps, using the Mehrotra predictor-corrector approach, in the NT framework. We also provide an analytical and numerical comparison of several methods using different search directions, and suggest that the method using the NT direction is more robust than alternative methods.<\/jats:p>","DOI":"10.1137\/s105262349630060x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"769-796","source":"Crossref","is-referenced-by-count":177,"title":["On the Nesterov--Todd Direction in Semidefinite Programming"],"prefix":"10.1137","volume":"8","author":[{"given":"M. J.","family":"Todd","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K. C.","family":"Toh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R. H.","family":"T\u00fct\u00fcnc\u00fc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"F. Alizadeh,\n Combinatorial Optimization with Interior Point Methods and Semi\u2013definite Matrices\n , Ph.D. thesis, University of Minnesota, Minneapolis, MN, 1991."},{"key":"R2","unstructured":"F. Alizadeh,\n Semidefinite programming home page\n , http:\/\/rutcor.rutgers.edu\/\u223calizadeh\/sdp.html."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496304700"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(79)90179-4"},{"key":"R5","unstructured":"G. H. Golub and C. F. Van Loan,\n Matrix Computations\n , 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989."},{"key":"R6","unstructured":"C. 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Nemirovskii,\n Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms\n , SIAM, Philadelphia, PA, 1994.","DOI":"10.1137\/1.9781611970791"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1287\/moor.22.1.1"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495290209"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496300611"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"JosSturm, ShuzhongZhang, 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":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896303739"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1137\/1038003"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495296115"},{"key":"R24","unstructured":"Y. Zhang,\n private communication\n , University of Maryland Baltimore County, Baltimore, MD, 1996."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S105262349630060X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:56:33Z","timestamp":1787331393000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S105262349630060X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,8]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,8]]}},"alternative-id":["10.1137\/S105262349630060X"],"URL":"https:\/\/doi.org\/10.1137\/s105262349630060x","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,8]]}}}