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A Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems

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Abstract

In this paper, a full-Newton step Interior-Point Method for solving monotone Weighted Linear Complementarity Problem is designed and analyzed. This problem has been introduced recently as a generalization of the Linear Complementarity Problem with modified complementarity equation, where zero on the right-hand side is replaced with the nonnegative weight vector. With a zero weight vector, the problem reduces to a linear complementarity problem. The importance of Weighted Linear Complementarity Problem lies in the fact that it can be used for modelling a large class of problems from science, engineering and economics. Because the algorithm takes only full-Newton steps, the calculation of the step size is avoided. Under a suitable condition, the algorithm has a quadratic rate of convergence to the target point on the central path. The iteration bound for the algorithm coincides with the best iteration bound obtained for these types of problems.

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Acknowledgements

The work of the first author is supported by a Grant from Iran’s National Elites Foundation, Project No. 15/2080. The first and the fourth authors thank Sharif University of Technology for supporting this work. The first author would also like to thank the support from the University of Applied Sciences and Arts, Northwestern Switzerland. The second author would like to thank the support of Babeş-Bolyai University.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Soodabeh Asadi & Nezam Mahdavi-Amiri

  2. Institute for Data Science, School of Engineering, University of Applied Sciences and Arts Northwestern Switzerland, Windisch, Switzerland

    Soodabeh Asadi

  3. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, No. 1 Mihail Kogalniceanu Street, 400084, Cluj-Napoca, Romania

    Zsolt Darvay

  4. Department of Mathematics, US Naval Academy, Annapolis, MD, USA

    Goran Lesaja

  5. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, USA

    Goran Lesaja

  6. Department of Mathematics and Statistics, University of Maryland, Baltimore County, MD, USA

    Florian Potra

Authors
  1. Soodabeh Asadi
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  2. Zsolt Darvay
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  3. Goran Lesaja
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  4. Nezam Mahdavi-Amiri
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  5. Florian Potra
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Corresponding author

Correspondence to Goran Lesaja.

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Communicated by Nobuo Yamashita.

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Asadi, S., Darvay, Z., Lesaja, G. et al. A Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems. J Optim Theory Appl 186, 864–878 (2020). https://doi.org/10.1007/s10957-020-01728-4

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  • DOI: https://doi.org/10.1007/s10957-020-01728-4

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