%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/