%A M. V. Solodov
%A P. Tseng
%T Modified Projection-Type Methods for Monotone Variational Inequalities
%D May 1994
%R 94-04
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X We propose new methods for solving the
variational inequality problem where the
underlying function $F$ is monotone. These methods may be viewed as
projection-type methods in which the projection
direction is modified by a strongly monotone mapping of the form $I - \alpha F$
or, if $F$ is affine with underlying matrix $M$, of the form $I+ \alpha M^T$, wi
th $\alpha \in (0,\infty)$. We show that these methods are globally convergent
and, if in addition a certain error bound based on the natural residual holds lo
cally, the convergence is linear.
Computational experience comparing the new methods with the extragradient
method is reported.