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New Complexity Analysis of the Primal–Dual Method for Semidefinite Optimization Based on the Nesterov–Todd Direction

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Abstract

Interior-point methods for semidefinite optimization have been studied intensively in recent times, due to their polynomial complexity and practical efficiency. In this paper, first we present some technical results about symmetric matrices. Then, we apply these results to give a unified analysis for both large update and small update interior-point methods for SDP based on the Nesterov–Todd (NT) direction.

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Authors and Affiliations

  1. Faculty of Information Technology and Systems, Delft University of Technology, Delft, Netherlands

    J. PENG (Ph.D.)

  2. Faculty of Information Technology and Systems, Delft University of Technology, Delft, Netherlands

    C. ROOS (Professor)

  3. Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

    T. TERLAKY (Professor)

Authors
  1. J. PENG
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  2. C. ROOS
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  3. T. TERLAKY
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PENG, J., ROOS, C. & TERLAKY, T. New Complexity Analysis of the Primal–Dual Method for Semidefinite Optimization Based on the Nesterov–Todd Direction. Journal of Optimization Theory and Applications 109, 327–343 (2001). https://doi.org/10.1023/A:1017514422146

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  • DOI: https://doi.org/10.1023/A:1017514422146

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