An improved Goldstein's type method for a class of variant variational inequalities

This paper aims at presenting an improved Goldstein's type method for a class of variant variational inequalities. In particular, the iterate computed by an existing Goldstein's type method [He, A Goldstein's type projection method for a class of variant variational inequalities J. Comput. Math. 17(4) (1999) 425–434]. is used to construct a descent direction, and thus the new method generates the new iterate by searching the optimal step size along the descent direction. Some restrictions on the involving functions of the existing Goldstein's type methods are relaxed, while the global convergence of the new method is proved without additional assumptions. The computational superiority of the new method is verified by the comparison to some existing methods.