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Complexity Analysis of a Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems

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  • Behrouz Kheirfam

    (Azarbaijan Shahid Madani University)

Abstract

In this paper, we present a full-Newton step interior-point method for solving monotone Weighted Linear Complementarity Problem. We use the technique of algebraic equivalent transformation (AET) of the nonlinear equation of the system which defines the central path. The AET is based on the square root function which plays an important role in computing the new search directions. The algorithm uses only full-Newton steps at each iteration, and hence, line searches are no longer needed. We prove that the algorithm has a quadratic rate of convergence to the target point on the central path. The obtained iteration bound coincides with the best known iteration bound for these types of problems.

Suggested Citation

  • Behrouz Kheirfam, 2024. "Complexity Analysis of a Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 133-145, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02139-3
    DOI: 10.1007/s10957-022-02139-3
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    References listed on IDEAS

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    1. 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.
    2. G. Q. Wang & Y. Q. Bai, 2012. "A New Full Nesterov–Todd Step Primal–Dual Path-Following Interior-Point Algorithm for Symmetric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 966-985, September.
    3. Behrouz Kheirfam, 2013. "A new infeasible interior-point method based on Darvay’s technique for symmetric optimization," Annals of Operations Research, Springer, vol. 211(1), pages 209-224, December.
    4. Jingyong Tang & Jinchuan Zhou, 2021. "Quadratic convergence analysis of a nonmonotone Levenberg–Marquardt type method for the weighted nonlinear complementarity problem," Computational Optimization and Applications, Springer, vol. 80(1), pages 213-244, September.
    5. Florian A. Potra, 2016. "Sufficient weighted complementarity problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 467-488, June.
    6. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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