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A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions

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Abstract

We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are \(C^1\). Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.

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Acknowledgments

The authors are much indebted to the anonymous referee for the constructive comments and useful suggestions which improved the presentation of the paper considerably. The research of the 1st author is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The postdoctoral fellowship of the 2nd author is supported by NSERC.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, V2C 0C8, BC, Canada

    Mohamed A. Tawhid, Wei-Zhe Gu & Benjamin Tran

  2. Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bey, Alexandria, 21511, Egypt

    Mohamed A. Tawhid

  3. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, People’s Republic of China

    Wei-Zhe Gu

Authors
  1. Mohamed A. Tawhid
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  2. Wei-Zhe Gu
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  3. Benjamin Tran
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Correspondence to Mohamed A. Tawhid.

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Communicated by Ernesto G. Birgin.

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Tawhid, M.A., Gu, WZ. & Tran, B. A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions. Comp. Appl. Math. 37, 1–26 (2018). https://doi.org/10.1007/s40314-016-0328-6

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  • DOI: https://doi.org/10.1007/s40314-016-0328-6

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