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On the extension of an arc-search interior-point algorithm for semidefinite optimization

  • * Corresponding author: Behrouz Kheirfam

    * Corresponding author: Behrouz Kheirfam 
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  • This paper concerns an extension of the arc-search strategy that was proposed by Yang [26] for linear optimization to semidefinite optimization case. Based on the Nesterov-Todd direction as Newton search direction it is shown that the complexity bound of the proposed algorithm is of the same order as that of the corresponding algorithm for linear optimization. Some preliminary numerical results indicate that our primal-dual arc-search path-following method is promising for solving the semidefinite optimization problems.

    Mathematics Subject Classification: 90C51.

    Citation:

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  • Table 1.  Numerical results for Example 1

    $\varepsilon$ MTYAlgor NewAlgor
    Iter. CPU DGAP Iter. CPU DGAP
    $10^{-6}$ 55 0.1882 $4.4981e^{-6}$ 11 0.0729 $2.1703e^{-6}$
    $10^{-8}$ 73 0.2476 $4.7261e^{-8}$ 13 0.0679 $9.6585e^{-9}$
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    Table 2.  Numerical results for Example 2

    $n\times m$ MTYAlgor NewAlgor
    Iter. CPU Iter. CPU
    $10\times20$ 97.2 3.4915 28.8 1.1028
    $30\times30$ 117.3 18.7385 32.3 5.9383
    $25\times40$ 116.2 67.5448 33.7 23.2533
    $40\times20$ 115.9 70.7626 33.1 24.0481
    $50\times50$ 136.7 179.9818 35.4 87.9356
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