On strictly semi-monotone (semi-monotone) properties in nonsmooth functions

This paper deals with characterizations of strictly semi-monotone (semi-monotone) properties in nonsmooth functions that are H-differentiable. These results give a unified treatment of such results for C1-functions, semi-smooth functions, and for locally Lipschitzian functions. Illustrations to nonlinear complementarity problems are given to show the usefulness of our results.