Abstract: A class of new generalized convex function,strongly semi-G-preinvex function,is given in this paper.It is an important class ofgeneralized convex function.It is a true generalization of semi-preinvex functions and strongly G-preinvex functions.First,an example is given to show that there exists strongly semi-G-preinvex function.At the same time,an example is given to show that strongly semi-G-preinvex function is different from strongly preinvex functions.Then,some properties of strongly semi-G-preinvex functions are discussed.Finally,some optimal results are obtained in nonlinear programming problems,and an example is also given for illustration of the corresponding results.

Key words: semi-connected sets, nonlinear programming, stronglypreinvex functions, strongly semi-G-preinvex functions