Merit Functions for Complementarity and Related Problems: A Survey
Computational Optimization and Applications
Smooth Convex Approximation to the Maximum Eigenvalue Function
Journal of Global Optimization
A New Path-Following Algorithm for Nonlinear P*Complementarity Problems
Computational Optimization and Applications
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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.