Necessary Optimality Condition for Nonlinear Interval Vector Programming Problem Under B-Arcwise Connected Functions

We consider the nonlinear interval vector programming problem (NIVP) for solving uncertainty programming problems and introduced the set of B-arcwise connected interval-valued function (BCIF) and strictly BCIF (SBCIF) by generalizing the notion of arcwise connected interval-valued function. Arcwise connected function is a generalization of convex function which is defined on the arcwise connected set [2]. The differentiability of the function is studied by introducing right generalized Hukuhara derivative (gH-derivative or gH-differentiable). The extremum conditions for the functions under right gH-derivative have been derived. This is a new type of NIVP with right gH-differentiable function in both multiple objective and constraints involving BCIFs. The Fritz-John kind and Karush-Kuhn-Tucker kind necessary weakly LU-efficiency condition for NIVP are obtained with right gH-differentiable BCIFs in both multiple objective function and constraints functions.