A hybrid Newton method for solving the variational ... - CiteSeerX
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A hybrid Newton method for solving the variational ... - CiteSeerX
May 5, 1997 - with y (x) := 5X(x 0 01F(x)) and 5X(1) being the projection operator onto ... g (x): (4). When the mapping F is di erentiable, the D-gap function g is ...
A hybrid Newton method for solving the variational inequality problem via the D-gap function J.M. Peng
2
M. Fukushima
1
3
2
State Key Laboratory of Scienti c and Engineering Computing Institute of Computational Mathematics and Scienti c/Engineering Computing Academic Sinica, Beijing, P. O. Box 2719, 100080, China 3
Department of Applied Mathematics and Physics Graduate School of Engineering, Kyoto University, Kyoto 606-01, Japan
May 5, 1997
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.
