Abstract
A condition for global convergence of a homotopy method for a variational inequality problem (VIP) on an unbounded set is introduced. The condition is derived from a concept of a solution at infinity to VIP. By an argument of the existence of a homotopy path, we show that VIP has a solution if it has no solution at infinity. It is proved that if any of several well-known conditions given in the literature holds, there is no solution at infinity. Furthermore, a globally convergent homotopy method is developed to compute a solution to VIP. Several numerical examples illustrate how to follow the homotopy path starting at an arbitrary point in the unbounded set.
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