スレーターの制約想定のもとでの変分不等式に対する連続変形法

抄録

The continuation method is one approach to solve the system of nonlinear equations. For variational inequality problems, interior point like continuation methods based on the KKT conditions for VIP have been proposed. Kanzow and Jiang considered one parameter continuation method for strongly monotone variational inequality problems and showed that a continuation path exists under the linear independence constraint qualification condition. In this paper, we show that, the unique continuation path approaching to a solution exists for strongly monotone problems under the Slater's constraint qualification instead of the linear independence constraint qualification. Moreover, this theorem is shown to give another proof of the existence theorem for a continuation path of Chen and Harker.