A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming - Hehua Jiao; Sanyang Liu; Xinying Pai (Journal of Applied Mathematics)
A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-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.