In the paper, we introduce the concepts of G-type I and generalized G-type I
functions for a new class of nonconvex multiobjective variational control problems. For
such nonconvex vector optimization problems, we prove sufficient optimality conditions for
weakly efficiency, efficiency and properly efficiency under assumptions that the functions
constituting them are G-type I and/or generalized G-type I objective and constraint functions.
Further, for the considered multiobjective variational control problem, its dual multiobjective
variational control problem is given and several duality results are established under
(generalized) G-type I objective and constraint functions.