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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    M. Sayadi Shahraki

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran

    H. Mansouri & M. Zangiabadi

  3. Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    N. Mahdavi-Amiri

Authors
  1. M. Sayadi Shahraki
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  2. H. Mansouri
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  3. M. Zangiabadi
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  4. N. Mahdavi-Amiri
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Correspondence to H. Mansouri.

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Sayadi Shahraki, M., Mansouri, H., Zangiabadi, M. et al. A wide neighborhood primal-dual predictor-corrector interior-point method for symmetric cone optimization. Numer Algor 78, 535–552 (2018). https://doi.org/10.1007/s11075-017-0387-9

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  • DOI: https://doi.org/10.1007/s11075-017-0387-9

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