On some projection and contraction methods for solving monotone variational inequalities

Variational inequalities play a significant role in mathematical programming and have been studied by many researchers. Recently, some iterative projection and contraction (PC) methods for solving monotone variational inequalities were presented. The efficiency of the methods depends essentially on the search directions. In this paper, the author points out that the search directions of existing PC methods are based on various combinations of three fundamental inequalities. This will offer orientation for constructing more efficient PC methods.