Structural and Stability Properties of P ₀ Nonlinear Complementarity Problems

We consider P₀ nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the Mountain Pass Theorem to a smooth reformulation of the complementarity problem. We show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique. Furthermore, we prove that a solution is stable in Ha's sense if and only if it is globally unique, while the complementarity problem is stable if and only if the solution set is bounded.