We consider an optimal control problem governed by a system of nonlinear difference equations. We obtain the existence of the optimal control as well as first-order optimality conditions of Pontryagin type by using the Dubovitskii–Milyutin formalism. Also, we give the necessary and sufficient conditions for global optimality.

We define a new class of optimal control problems and show that this class is the largest one of control problems where every admissible process that satisfies the Extended Pontryaguin Maximum Principle is an optimal solution of nonregular optimal control problems. In this class of problems the local and global minimum coincide. A dual problem is also proposed, which may be seen as a generalization of the Mond–Weir-type dual problem, and it is shown that the 2-invexity notion is a necessary and sufficient condition to establish weak, strong, and converse duality results between a nonregular optimal control problem and its dual problem. We also present an example to illustrate our results.

In this work sufficient conditions are established to ensure that all feasible points are (properly) efficient solutions in non trivial situations, for a class of non-differentiable, non-convex multiobjective minimization problems. Considering locally Lipschitz functions and some results of non-differentiable analysis introduced by F. H. Clarke.