%0 Journal Article
%T A Class of Semilocal -Preinvex Functions and Its Applications in Nonlinear Programming
%A Hehua Jiao
%A Sanyang Liu
%A Xinying Pai
%J Journal of Applied Mathematics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/629194
%X A kind of generalized convex set, called as local star-shaped -invex set with respect to , is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal -preinvex functions, which is a generalization of semi--preinvex functions and semilocal -convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
%U http://www.hindawi.com/journals/jam/2012/629194/