Properties of a homotopy solution path for complementarity problems with quasi-monotone mappings

摘要

We study several properties of a homotopy solution path associated with continuous nonlinear quasi-monotone complementarity problems. We use Poincare-Bohn’s homotopy invariance theorem of degree to derive an alternative theorem. Based on this result, a sufficient condition is established to assure the existence and boundedness of this homotopy solution path. Our results provide a theoretical basis to develop a new computational method for quasi-monotone complementarity problems.