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.