Analysis for a homotopy path of complementarity problems based on μ-exceptional family

This paper is concerned with several structural properties of a homotopy path for nonlinear continuous semi-monotone complementarity problems. Especially, several sufficient conditions are established for the existence and boundedness of this homotopy path. Under the P0 property, all these sufficient conditions guarantee the uniqueness and continuity of this path. The concept of μ-exceptional family plays a key role in the analysis throughout this paper.