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New parameterized kernel functions for linear optimization

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  • Yanqin Bai
  • Wei Xie
  • Jing Zhang

Abstract

Recent studies on the kernel function-based primal-dual interior-point algorithms indicate that a kernel function not only represents a measure of the distance between the iteration and the central path, but also plays a critical role in improving the computational complexity of an interior-point algorithm. In this paper, we propose a new class of parameterized kernel functions for the development of primal-dual interior-point algorithms for solving linear programming problems. The properties of the proposed kernel functions and corresponding parameters are investigated. The results lead to a complexity bounds of $${O\left(\sqrt{n}\,{\rm log}\,n\,{\rm log}\,\frac{n}{\epsilon}\right)}$$ for the large-update primal-dual interior point methods. To the best of our knowledge, this is the best known bound achieved. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Yanqin Bai & Wei Xie & Jing Zhang, 2012. "New parameterized kernel functions for linear optimization," Journal of Global Optimization, Springer, vol. 54(2), pages 353-366, October.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:353-366
    DOI: 10.1007/s10898-012-9934-z
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    Cited by:

    1. Peng, Wei, 2021. "The transmission of default risk between banks and countries based on CAViaR models," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 500-509.

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