Two new self-adaptive projection methods for variational inequality problems

In this paper, we propose two new projection methods for solving variational inequality problems (VI). The method is simple; it uses only function evaluation and projection onto the feasible set. Under the conditions that the underlying function is continuous and satisfies some generalized monotonicity assumption, the methods are proven to converge to a solution of variational inequality globally. Some preliminary computational results are reported to illustrate the efficiency of the methods.