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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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
Keywords
- Generalized complementarity problem
- GCP function
- Generalized FB function
- Unconstrained minimization
- Regularity conditions
- Merit function
- Descent algorithm