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.
维普
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