Advanced Search

The question of Lipschitz continuity of solutions to parameterized variational inequalities with perturbed constraint sets is considered. Under the sole Lipschitz continuity assumption on data, a Lipschitz continuity result is proved which, in particular, holds for variational inequalities modeling evolutionary network equilibrium problems. Moreover, in view of real-life applications, a long-term memory is introduced and the corresponding variational inequality model is discussed.

We provide a sensitivity result for the solutions to the following finite-dimensional quasi-variational inequality $$QVIu\in K\left(u\right),〈C\left(u\right),v-u〉\ge 0,\mathrm{\forall }v\in K\left(u\right),$$ when both the operator $C$ and the convex $K$ are perturbed. In particular, we prove the Hölder continuity of the solution sets of the problems perturbed around the original problem. All the results may be extended to infinite-dimensional (QVI).