%0 Journal Article
%T Strongly Semi-G-preinvex Functions and Its Properties
%A PENG Zai-yun
%A KONG Xiang-xi
%J Journal of Chongqing Normal University
%D 2013
%I Chongqing Normal University
%X 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 S¦Á={x¡ÊX:f(x)¡Ü¦Á}, epigraph Ef={(x,¦Á):x¡ÊX,¦Á¡ÊR,f(x)¡Ü¦Á}. At the same time, a judging theorem of strongly semi-G-preinvex functions is given. Finally, an application of strongly ¡¼JP¡½semi-G-preinvexity is obtained in nonlinear programming problems: for a class of restrained optimization (P), let y¡ÊD is a optimum of (P), let f is a strongly semi-G-preinvex functions on -D-, restrained function gi,i¡ÊJ is a strongly semi-Gi-preinvex functions on D, then y is unique. Then examples are given for illustration of the corresponding results.
%K semi-connected sets£»nonlinear programming£»semi-G-preinvex functions£»strongly semi-G-preinvex functions
%U http://journal.cqnu.edu.cn/1302/pdf/130201.pdf