{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:29:59Z","timestamp":1787333399898,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[1998,8]]},"abstract":"<jats:p>The theory of self-concordance in convex optimization has been used to analyze the complexity of interior-point methods based on Newton's method. For large problems, it may be impractical to use Newton's method; here we analyze a truncated-Newton method, in which an approximation to the Newton search direction is used. In addition, practical interior-point methods often include enhancements such as extrapolation that are absent from the theoretical algorithms analyzed previously. We derive theoretical results that apply to such an algorithm, one similar to a sophisticated computer implementation of a barrier method. The results for a single barrier subproblem are a satisfying extension of the results for Newton's method. When extrapolation is used in the overall barrier method, however, our results are more limited. We indicate (by both theoretical arguments and examples) why more elaborate results may be difficult to obtain.<\/jats:p>","DOI":"10.1137\/s1052623496306620","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"833-849","source":"Crossref","is-referenced-by-count":18,"title":["On the Complexity of a Practical Interior-Point Method"],"prefix":"10.1137","volume":"8","author":[{"given":"Stephen G.","family":"Nash","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ariela","family":"Sofer","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":"10.1007\/BF02206826"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0805008"},{"key":"R3","unstructured":"A. S. Nemirovskii,\n                      Interior Point Polynomial Time Methods in Convex Programming\n                      , Lecture notes, Faculty of Industrial Engineering and Management, Technion\u2014The Israel Institute of Technology, 1994."},{"key":"R3","unstructured":"NesNY. Nesterov and A. S. Nemirovskii, Interior\u2010Point Polynomial Algorithms in Convex Programming SIAM Philadelphia 1994 NesTY. E. Nesterov and M. J. Todd, Primal\u2010dual interior point methods for self\u2010scaled cones, SIAM J. Optim. 8 1998 324\u2013364"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1080\/10556789808805691"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(98)00014-5"},{"key":"R6","unstructured":"MargaretWright, Interior methods for constrained optimization, Acta Numer., Cambridge Univ. Press, Cambridge, 1992, 341\u201340793d:90037"},{"key":"R7","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\/S1052623496306620","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:56:48Z","timestamp":1787331408000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1052623496306620"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,8]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,8]]}},"alternative-id":["10.1137\/S1052623496306620"],"URL":"https:\/\/doi.org\/10.1137\/s1052623496306620","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,8]]}}}