Preprint A23/2001
A class of globally convergent algorithms for pseudomonotone variational inequalities

Mikhail Solodov

**Keywords: **
variational inequalities

We describe a fairly broad class of algorithms for
solving variational inequalities, global convergence of which is
based on the strategy of generating a hyperplane
separating the current iterate from the solution set.
The methods are shown to converge under very mild assumptions.
Specifically, the problem mapping is only assumed to be
continuous and pseudomonotone with respect to at least one
solution. The strategy to obtain (super)linear rate of
convergence is also discussed. The algorithms in this class
differ in the tools which are used to construct the
separating hyperplane. Our general scheme subsumes
an extragradient-type projection method, a globally
and locally superlinearly convergent Josephy-Newton-type method,
a certain minimization-based method, and a splitting technique.