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A new second-order corrector interior-point algorithm for semidefinite programming

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  • Changhe Liu
  • Hongwei Liu

Abstract

In this paper, we propose a second-order corrector interior-point algorithm for semidefinite programming (SDP). This algorithm is based on the wide neighborhood. The complexity bound is $${O(\sqrt{n}L)}$$ for the Nesterov-Todd direction, which coincides with the best known complexity results for SDP. To our best knowledge, this is the first wide neighborhood second-order corrector algorithm with the same complexity as small neighborhood interior-point methods for SDP. Some numerical results are provided as well. Copyright Springer-Verlag 2012

Suggested Citation

  • Changhe Liu & Hongwei Liu, 2012. "A new second-order corrector interior-point algorithm for semidefinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 165-183, April.
    • Handle: RePEc:spr:mathme:v:75:y:2012:i:2:p:165-183
    DOI: 10.1007/s00186-012-0379-4
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
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