Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #97005 (May, 1997)

A hybrid Newton method for solving the variational inequality problem via the D-gap function
by Jiming Peng and Masao Fukushima

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.