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Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term

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  • X. Z. Cai
  • G. Q. Wang
  • M. El Ghami
  • Y. J. Yue

Abstract

We introduce a new parametric kernel function, which is a combination of the classic kernel function and a trigonometric barrier term, and present various properties of this new kernel function. A class of large- and small-update primal-dual interior-point methods for linear optimization based on this parametric kernel function is proposed. By utilizing the feature of the parametric kernel function, we derive the iteration bounds for large-update methods, , and small-update methods, . These results match the currently best known iteration bounds for large- and small-update methods based on the trigonometric kernel functions.

Suggested Citation

  • X. Z. Cai & G. Q. Wang & M. El Ghami & Y. J. Yue, 2014. "Complexity Analysis of Primal-Dual Interior-Point Methods for Linear Optimization Based on a New Parametric Kernel Function with a Trigonometric Barrier Term," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, June.
    • Handle: RePEc:hin:jnlaaa:710158
    DOI: 10.1155/2014/710158
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