We mainly discuss the properties and applications of semi-G-preinvexity, which was introduced in Peng and Chang 2013. Examples are given to show the existence of semi-G-preinvex functions. Three important properties and characterizations of semi-G-preinvex functions are established. Furthermore, under semi-G-preinvexity, some optimality results are obtained in nonlinear programming problems with inequality constraint. Our results improve and generalize some known results

Kai Zhi Yu