Semistrict G -Preinvexity and Optimality in Nonlinear Programming

Abstract

A class of semistrictly $G$-preinvex functions and optimality in nonlinear programming are further discussed. Firstly, the relationships between semistrictly $G$-preinvex functions and $G$-preinvex functions are further discussed. Then, two interesting properties of semistrictly $G$-preinvexity are given. Finally, two optimality results for nonlinear programming problems are obtained under the assumption of semistrict $G$-preinvexity. The obtained results are new and different from the corresponding ones in the literature. Some examples are given to illustrate our results.