The paper investigates a linear homotopy F(ë,t) connecting an appropriate smooth equation G=0 with Kojima’s (nonsmooth) system K=0 describing critical points (primal-dual) of a nonlinear optimization problem (NLP) in finite dimension. For t=0, the present system may be seen e.g. as a starting system for an embedding procedure to determine a critical point to NLP. For t≅1, it may be regarded as a regularization of K. Conditions for regularity (necessary and sufficient) and solvability (sufficient) are studied. Though, formally, they can be given in a unified way, the paper shows that their meaning differs for t<1 and t=1. Particularily, no MFCQ-like condition must be imposed in order to ensure regularity for t<1.
