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Paper   IPM / M / 14729
School of Mathematics
  Title:   A primal-dual predictor-corrector interior-point method for symmetric cone programming with O(√rlogε−1) iteration complexity
  Author(s):  M. Sayadi Shahraki (Joint with H. mansouri and M. Zangiabadi)
  Status:   Published
  Journal: International Journal of Computer Mathematics
  Vol.:  94
  Year:  2017
  Pages:   1998-2010
  Supported by:  IPM
‎In this paper,we propose a new predictor-corrector interior-point‎ ‎method for symmetric cone programming‎. ‎This algorithm is based on‎ ‎a wide neighborhood and the Nesterov-Todd direction‎. ‎We prove‎ ‎that‎, ‎besides the predictor steps‎, ‎each corrector step also‎ ‎reduces the duality gap by a rate of‎ ‎1−[1/(O\br√r)]‎, ‎where r is the rank of the‎ ‎associated Euclidean Jordan algebras‎. ‎In particular‎, ‎the‎ ‎complexity bound is O\br√r logε−1‎, ‎where ε > 0 is a given tolerance‎. ‎To our knowledge‎, ‎this is the best complexity result obtained so far for‎ ‎interior-point methods with a wide neighborhood over symmetric‎ ‎cones‎. ‎The numerical results show that the proposed algorithm is effective‎.

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