In this paper the KKT system of a general variational inequality problem (denoted by VIP(X,F)) is reformulated as a constrained optimization problem. A sufficient condition, which ensures a stationary point of the optimization problem being a solution of the KKT system of VIP(X,F), is analyzed. A projection-type method for solving the KKT system of VIP(X,F) with closed convex set $X$ is presented. The new algorithm has nice properties such as retaining feasibility, easy computation if the region $X$ is a box or a ball, and strongly global and local convergence. Numerical examples show that the new algorithm is promising.
"A feasible method for solving the KKT system of variational inequalities." Hokkaido Math. J. 35 (1) 87 - 105, February 2006. https://doi.org/10.14492/hokmj/1285766309