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A predictor-corrector algorithm for linear optimization based on a modified Newton direction

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Abstract

We present a predictor-corrector algorithm for linear optimization based on a modified Newton direction. In each main iteration, the algorithm operates two kinds of steps: a modified Newton step and a damped predictor step. The modified Newton step is generated from an equivalent reformulation of the centering equation from the system, which defines the central path, and move in the direction of a small neighborhood of the central path. While the damped predictor step is used to move in the direction of optimal solution and reduce the duality gap. The procedure is repeated until an ϵ-approximate solution is found. We derive the complexity for the algorithm, and obtain the best-known result for linear optimization.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Sci-Tech University, Zhejiang, 310018, China

    Yinghong Xu

  2. Department of Mathematics, Zhejiang A&F University, Zhejiang, 311300, China

    Lipu Zhang & Zhengjing Jin

Authors
  1. Yinghong Xu
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  2. Lipu Zhang
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  3. Zhengjing Jin
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Corresponding author

Correspondence to Yinghong Xu.

Additional information

Xu’s research is supported by the Natural Science Foundation of Zhejiang Province No. Q12A010085. Zhang’s research is supported by the grant from National Natural Science Foundation of China No. 11171373.

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Xu, Y., Zhang, L. & Jin, Z. A predictor-corrector algorithm for linear optimization based on a modified Newton direction. J. Appl. Math. Comput. 40, 73–86 (2012). https://doi.org/10.1007/s12190-012-0553-0

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  • DOI: https://doi.org/10.1007/s12190-012-0553-0

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