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New parameterized kernel functions for linear optimization

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  • Yanqin Bai

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  • Wei Xie
  • Jing Zhang
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    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

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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 2 (October)
    Pages: 353-366

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:353-366

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    Web page: http://www.springer.com/business/operations+research/journal/10898

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    Related research

    Keywords: Linear programming; Primal-dual interior-point method; Large-update methods; 60K05; 90C51;

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