On interval valued functions and Mangasarian type duality involving Hukuhara derivative

In this paper, we introduce twice weakly differentiable and twice H-diferentiable interval valued functions. The existence of twice H-differentiable interval-valued function and its relation with twice weakly differentiable functions are presented. Interval valued bonvex and generalized bonvex functions involving twice H-differentiability are proposed. Under the proposed settings, necessary conditions are elicited naturally in order to achieve LU-efficient solution. Mangasarian type dual is discussed for a nondifferentiable multiobjective programming problem and appropriate duality results are also derived. The theoretical developments are illustrated through non-trivial numerical examples.