# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 35 (2006) pp.87-105

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### Abstract

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.

MSC(Primary) 90C33 90C30, 65H10 Variational inequality problem, KKT system, projection method, global andb local convergence