We propose a new projection algorithm for solving the variational inequalit
y problem, where the underlying function is continuous and satisfies a cert
ain generalized monotonicity assumption (e.g., it can be pseudomonotone). T
he method is simple and admits a nice geometric interpretation. It consists
of two steps. First, we construct an appropriate hyperplane which strictly
separates the current iterate from the solutions of the problem. This proc
edure requires a single projection onto the feasible set and employs an Arm
ijo-type linesearch along a feasible direction. Then the next iterate is ob
tained as the projection of the current iterate onto the intersection of th
e feasible set with the halfspace containing the solution set. Thus, in con
trast with most other projection-type methods, only two projection operatio
ns per iteration are needed. The method is shown to be globally convergent
to a solution of the variational inequality problem under minimal assumptio
ns. Preliminary computational experience is also reported.