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Adaptive Large-Neighborhood Self-Regular Predictor-Corrector Interior-Point Methods for Linear Optimization

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  • M. Salahi

    (McMaster University)

  • T. Terlaky

    (McMaster University)

Abstract

It is known that predictor-corrector methods in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. The best iteration bound based on the classical logarithmic barrier function is O(nlog (n/∊)). In this paper, we propose a family of self-regular proximity-based predictor-corrector (SRPC) IPMs for LO in a large neighborhood of the central path. In the predictor step, we use either an affine scaling or a self-regular direction; in the corrector step, we use always a self-regular direction. Our new algorithms use a special proximity function with different search directions and thus allows us to improve the so far best theoretical iteration complexity for a family of SRPC IPMs. An O $$(\sqrt{n}{\exp} ((1 - q + {\log} n)/2) {\log} n {\log} (n/\epsilon))$$ worst-case iteration bound with quadratic convergence is established, where q is the barrier degree of the SR proximity function.

Suggested Citation

  • M. Salahi & T. Terlaky, 2007. "Adaptive Large-Neighborhood Self-Regular Predictor-Corrector Interior-Point Methods for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 143-160, January.
  • Handle: RePEc:spr:joptap:v:132:y:2007:i:1:d:10.1007_s10957-006-9095-7
    DOI: 10.1007/s10957-006-9095-7
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
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