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Under an assumption of primal and dual strict feasibility, we show that the primal and dual central paths exist and converge to the analytic centers of the optimal faces of, respectively, the primal and the dual problems. We consider a class of trajectories that are similar to the central path but can be constructed to pass through any given interior feasible or infeasible point, and study their convergence. Finally, we study the derivatives of these trajectories and their convergence.<\/jats:p>","DOI":"10.1137\/s105262349630009x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"871-886","source":"Crossref","is-referenced-by-count":41,"title":["Interior Point Trajectories in Semidefinite Programming"],"prefix":"10.1137","volume":"8","author":[{"given":"D.","family":"Goldfarb","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Scheinberg","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\/BF01594923"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0805002"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(96)00079-2"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496304700"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1975.57.15"},{"key":"R6","first-page":"499","volume":"314","author":"Bayer D. 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Mehrotra,\n                      Higher Order Methods and Their Performance\n                      , Technical Report 90\u201016R1, Dept. of IE and MS, Northwestern Univ., Evanson, IL, 1991."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495293056"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1287\/moor.15.2.191"},{"key":"R21","unstructured":"Yu. E. Nesterov and A. S. Nemirovskii,\n                      Interior point Methods in Convex Programming: Theory and Application\n                      , SIAM, Philadelphia, PA, 1994."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1287\/moor.22.1.1"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495290209"},{"key":"R24","unstructured":"G. Pataki,\n                      On the Facial Structure of Cone\u2010LP\u2019s and Semi\u2010definite Programs\n                      , Research Report MSRR\u2010595, Graduate School of Industrial Administration, Carnegie Mellon Univ., Pittsburgh, PA, 1994."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021700210959"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623495288350"},{"key":"R27","unstructured":"K. Scheinberg,\n                      Issues in Interior Point Methods in Semidefinite and Linear Programming\n                      , Ph.D. thesis, Columbia University, New York, 1996."},{"key":"R28","unstructured":"M. Shida and S. Shindoh,\n                      Monotone Semidefinite Complementarity Problems\n                      , Working Paper B\u2010312, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Japan, 1996."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5610(94)00062-X"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1137\/1038003"},{"key":"R31","unstructured":"Y. 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