Optimality conditions and duality results for a class of differentiable vector optimization problems with the multiple interval-valued objective function

In this paper, a differentiable interval-valued vector optimization problem with the multiple objective function and with both inequality and equality constraints is considered. The Karush-Kuhn-Tucker necessary optimality conditions are established for a weak LU-Pareto solution in the considered vector optimization problem with the multiple interval-objective function under the Kuhn-Tucker constraint qualification. Further, the sufficient optimality conditions for a (weak) LU-Pareto solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered differentiable vector optimization problem with the multiple interval-objective function are (F, rho)-convex.