Numerical Algorithms

, Volume 78, Issue 2, pp 535–552 | Cite as

A wide neighborhood primal-dual predictor-corrector interior-point method for symmetric cone optimization

  • M. Sayadi Shahraki
  • H. Mansouri
  • M. Zangiabadi
  • N. Mahdavi-Amiri
Original Paper


We present a primal-dual predictor-corrector interior-point method for symmetric cone optimization. The proposed algorithm is based on the Nesterov-Todd search directions and a wide neighborhood, which is an even wider neighborhood than a given negative infinity neighborhood. At each iteration, the method computes two corrector directions in addition to the Ai and Zhang directions (SIAM J. Optim. 16, 400–417, 2005), in order to improve performance. Moreover, we derive the complexity bound of the wide neighborhood predictor-corrector interior-point method for symmetric cone optimization that coincides with the currently best known theoretical complexity bounds for the short step algorithm. Finally, some numerical experiments are provided to reveal the effectiveness of the proposed method.


Symmetric cone Euclidean Jordan algebra Predictor-corrector interior-point method Central path 


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The research of the first author was in part supported by a grant from IPM (No. 96900076). The second and third authors thank Shahrekord University and the fourth author thanks Research Council of Sharif University of Technology for financial support. The second and third authors were also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • M. Sayadi Shahraki
    • 1
  • H. Mansouri
    • 2
  • M. Zangiabadi
    • 2
  • N. Mahdavi-Amiri
    • 3
  1. 1.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of Applied Mathematics, Faculty of Mathematical SciencesShahrekord UniversityShahrekordIran
  3. 3.Department of Mathematical SciencesSharif University of TechnologyTehranIran

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