Sufficient optimality criteria and duality for multiobjective variational control problems with G-type I objective and constraint functions

Abstract

In the paper, we introduce the concepts of $$G$$G-type I and generalized $$G$$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 $$G$$G-type I and/or generalized $$G$$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) $$G$$G-type I objective and constraint functions.