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A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems

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  • Behrouz Kheirfam

    (Azarbaijan Shahid Madani University)

Abstract

In this paper, we first present a full-Newton step feasible interior-point algorithm for solving horizontal linear complementarity problems. We prove that the full-Newton step to the central path is quadratically convergent. Then, we generalize an infeasible interior-point method for linear optimization to horizontal linear complementarity problems based on new search directions. This algorithm starts from strictly feasible iterates on the central path of a perturbed problem that is produced by a suitable perturbation in the horizontal linear complementarity problem. We use the so-called feasibility steps that find strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, we obtain a strictly feasible iterate close enough to the central path of the new perturbed problem. The complexity of the algorithm coincides with the best known iteration bound for infeasible interior-point methods.

Suggested Citation

  • Behrouz Kheirfam, 2014. "A New Complexity Analysis for Full-Newton Step Infeasible Interior-Point Algorithm for Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 853-869, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0457-7
    DOI: 10.1007/s10957-013-0457-7
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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.
    2. Filiz Gurtuna & Cosmin Petra & Florian Potra & Olena Shevchenko & Adrian Vancea, 2011. "Corrector-predictor methods for sufficient linear complementarity problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 453-485, April.
    3. H. Mansouri & M. Pirhaji, 2013. "A Polynomial Interior-Point Algorithm for Monotone Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 451-461, May.
    4. G. Gu & H. Mansouri & M. Zangiabadi & Y. Q. Bai & C. Roos, 2010. "Improved Full-Newton Step O(nL) Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 271-288, May.
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    Cited by:

    1. Xiaoni Chi & Guoqiang Wang, 2021. "A Full-Newton Step Infeasible Interior-Point Method for the Special Weighted Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 108-129, July.

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