Abstract
Necessary conditions for optimal, or boundary solutions of differential inclusions usually state that such solutions are extremal in some sense. There are several possible concepts of extremality, which lead to different, often difficult to compare necessary conditions. In this paper, we give a complete comparison of three classes of extremal trajectories: two different Lagrange-type extremals, and Hamiltonian extremals. In the second part, we consider a nonconvex differential inclusion, and prove that every boundary trajectory is a Lagrangian extremal.
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