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A hybrid Newton method for solving the variational inequality problem via the D-gap function

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Abstract.

The variational inequality problem (VIP) can be reformulated as an unconstrained minimization problem through the D-gap function. It is proved that the D-gap function has bounded level sets for the strongly monotone VIP. A hybrid Newton-type method is proposed for minimizing the D-gap function. Under some conditions, it is shown that the algorithm is globally convergent and locally quadratically convergent.

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Authors and Affiliations

  1. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academic Sinica, Beijing, P.O. Box 2719, 100080, China. Current Address: Faculty of Technical Mathematics and Informatics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands, e-mail: j.peng@twi.tudelft.nl, , , , , , CN

    Ji-Ming Peng

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan, e-mail: fuku@kuamp.kyoto-u.ac.jp, , , , , , JP

    Masao Fukushima

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  1. Ji-Ming Peng
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  2. Masao Fukushima
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Received May 6, 1997 / Revised version received October 30, 1998¶Published online June 11, 1999

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Peng, JM., Fukushima, M. A hybrid Newton method for solving the variational inequality problem via the D-gap function. Math. Program. 86, 367–386 (1999). https://doi.org/10.1007/s101070050094

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  • DOI: https://doi.org/10.1007/s101070050094