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

[摘要] A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, andsome of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-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.

[学科分类] 应用数学