*(English)*Zbl 0955.90138

Summary: We consider the stability properties of solutions to parameterized nonlinear complementarity problems

where these are vector inequalities. We characterize the local upper Lipschitz continuity of the (possibly set-valued) solution mapping which assigns solutions $x$ to each parameter pair $(v,u)$. We also characterize when this solution mapping is locally a single-valued Lipschitzian mapping (so solutions exist, are unique, and depend Lipschitz continuously on the parameters). These characterizations are automatically sufficient conditions for the more general (and usual) case where $v=0$. Finally, we study the differentiability properties of the solution mapping in both the single-valued and set-valued cases, in particular obtaining a new characterization of $B$-differentiability in the single-valued case, along with a formula for the $B$-derivative. Though these results cover a broad range of stability properties, they are all derived from similar fundamental principles of variational analysis.

##### MSC:

90C33 | Complementarity and equilibrium problems; variational inequalities (finite dimensions) |

90C31 | Sensitivity, stability, parametric optimization |