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

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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.

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Acknowledgements

The author would like to thank the editor and anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Behrouz Kheirfam

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  1. Behrouz Kheirfam
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Correspondence to Behrouz Kheirfam.

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Communicated by Goran Lesaja.

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Kheirfam, B. Complexity Analysis of a Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems. J Optim Theory Appl 202, 133–145 (2024). https://doi.org/10.1007/s10957-022-02139-3

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