A Newton method for multiobjective optimization problems with interval-valued objective functions

In this study, we obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with interval-valued objective functions by applying Newton method. We consider a suitable partial ordering for a pair of intervals for attaining Pareto solutions of the MOP problem. We employ the generalized Hukuhara differentiability of interval-valued vector functions to derive Newton method. It is assumed that the objective functions of the interval-valued MOP are twice continuously generalized Hukuhara differentiable. Therefore, utilizing critical points of the related crisp problem, some necessary and sufficient conditions for weakly Pareto optimal solutions of an interval-valued MOP are obtained.