A new projection method for variational inequality problems

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.