A class of semilocal \(E\)-preinvex functions and its applications in nonlinear programming (Q411036)

Summary: A kind of generalized convex set, called as local star-shaped \(E\)-invex set with respect to \(\eta\), 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.