A Class of Semilocal E -Preinvex Functions and Its Applications in Nonlinear Programming

Abstract

A kind of generalized convex set, called as local star-shaped $E$-invex set with respect to $\mathrm{\eta ,}$ 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.