E-α-预不变凸区间值函数及最优性条件

E-α-Preinvex Interval Valued Function and Optimization Conditions

在LU序关系下获得了一类新的广义凸区间值函数——E-α-预不变凸区间值函数,并获得了相关性质及它的最优性条件。结合理论推导和例证,给出了例子验证E-α-预不变凸区间值函数的存在性;并讨论关于E-α-预不变凸区间值函数的基本性质,得到了E-可微情形下的必要条件;最后获得了在区间值约束情形下E-α-预不变凸区间值规划问题的最优性充分条件,并举例验证结论成立。研究将广义凸函数推广至E-α-预不变凸区间值情形,在一定程度上丰富了广义凸函数的研究,使它的应用性更加广泛。

A new class of generalized convex interval valued functions,E-α-preinvex interval valued functions,is obtained under the LU order relationship,and related properties and optimality conditions are obtained.Combining theoretical deduction and examples,an example is provided to verify the existence of E-α-preinvex interval valued functions,and the basic properties of E-α-preinvex interval valued functions are discussed.The necessary conditions for E-differentiable cases are obtained.Finally,the optimality sufficient conditions for the E-α-preinvex interval valued programming problem under interval valued constraints are obtained,and an example is given to verify the conclusion.This study extends generalized convex function to the case of E-α-preinvex interval valued function,which to some extent enriches the study of generalized convex functions and makes their applications more widespread.