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Complexity analysis of an interior-point algorithm for linear optimization based on a new proximity function

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Abstract

Kernel functions play an important role in the complexity analysis of the interior point methods for linear optimization. In this paper, we present a primal-dual interior point method for linear optimization based on a new kernel function consisting of a trigonometric function in its barrier term. By simple analysis, we show that the feasible primal-dual interior point methods based on the new proposed kernel function enjoys \(O\left (\sqrt {n}\left (\log {n}\right )^{2}\log \frac {n}{\epsilon }\right )\) worst case complexity result which improves the results obtained by El Ghami et al. (J Comput Appl Math 236:3613–3623, 2012) for the kernel functions with trigonometric barrier terms.

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Authors and Affiliations

  1. Department of Mathematics, K.N. Toosi Univ. of Tech., P.O. Box 16315-1618, Tehran, Iran

    M. Reza Peyghami & S. Fathi Hafshejani

  2. Scientific Computations in Optimization and Systems Engineering (SCOPE), K.N. Toosi Univ. of Tech., P.O. Box 16315-1618, Tehran, Iran

    M. Reza Peyghami & S. Fathi Hafshejani

Authors
  1. M. Reza Peyghami
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  2. S. Fathi Hafshejani
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Correspondence to M. Reza Peyghami.

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Peyghami, M.R., Hafshejani, S.F. Complexity analysis of an interior-point algorithm for linear optimization based on a new proximity function. Numer Algor 67, 33–48 (2014). https://doi.org/10.1007/s11075-013-9772-1

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  • DOI: https://doi.org/10.1007/s11075-013-9772-1

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