%0 Journal Article
%T An Equivalent Condition of Preinvex Function
%A ZHAO Ke-quan
%J Journal of Chongqing Normal University
%D 2010
%I Chongqing Normal University
%X Generalized convexity has been playing an important role in mathematical programming . In this paper, an equivalent condition of twice continuously differentiable preinvex function is established by transforming multivariate real-valued function into univariate real-valued function. Suppose that X be open invex set with respect to ¦Ç,¦Çsatisfies condition C , f be twice continuously differentiable and satisfies condition D. Then f is preinvex function with respect to ¦Ç,¦Çsatisfies condition C, f be twice continuously differentible and satisfiles condition D. then f is preinvex function with respect to ¦Ç if and only if ¦Íx,y¡ÊX,¦Ç(x,y)tV2f(x)¦Ç(x,y)¡Ý0. Our results provide new thoughts to verify the preinvexity of function and also generalize some known results.
%K generalized convexity
%K preinvex function
%K twice continuously differentiable function
%K equivalent condition
%U http://journal.cqnu.edu.cn/1003/pdf/0302.pdf