Strongly Semi-G-preinvex Functions and Its Properties

A class of new generalized convex function-strongly semi-G-preinvex functions, which is a true generalization of strongly preinvex functions and strongly -G-preinvex functions, is studied. First, an example is given to show that there exists a great deal of strongly semi-G-preinvex functions. Then, we discuss some properties of strongly semi-G-preinvex functions, get the relationships between strongly -G-preinvex functions f and it’s level-set Sα={x∈X:f(x)≤α}, epigraph Ef={(x,α):x∈X,α∈R,f(x)≤α}. At the same time, a judging theorem of strongly semi-G-preinvex functions is given. Finally, an application of strongly 〖JP〗semi-G-preinvexity is obtained in nonlinear programming problems: for a class of restrained optimization (P), let y∈D is a optimum of (P), let f is a strongly semi-G-preinvex functions on -D-, restrained function gi,i∈J is a strongly semi-Gi-preinvex functions on D, then y is unique. Then examples are given for illustration of the corresponding results.