A hybrid Newton method for solving the variational inequality problem via the D-gap function |
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| Authors: | Ji-Ming Peng Masao Fukushima |
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| Affiliation: | (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;(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 |
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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. Received May 6, 1997 / Revised version received October 30, 1998?Published online June 11, 1999 |
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| Keywords: | : variational inequality problem – D-gap function – Newton’ s method – unconstrained optimization – global convergence – quadratic convergence |
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