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.
| Original language | English |
|---|---|
| Pages (from-to) | 587-599 |
| Journal | Optimization Methods and Software |
| Volume | 22 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2007 |
Research Keywords
- Global convergence
- Homotopy method
- Variational inequality problems
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