LAGRANGIAN AND HAMILTONIAN NECESSARY CONDITIONS FOR THE GENERALIZED BOLZA PROBLEM AND APPLICATIONS

Our aim in this paper is to refine the well-known necessary optimality conditions for the general Bolza problem under a calmness assumption We prove Lagrangian and Hamiltonian necessary optimality conditions without standard convexity assumptions Our refinements consist in the utilization of a small subdifferential and in the presence of the maximum condition without convexity assumption on the velocities Our approach lies in reducing the generalized Bolza problem in an optimal control problem governed by bounded and measurably Lipschitz differential inclusions Out results allow its to simplify enough the proof of the maximum principle; to obtain a new Euler-Lagrange inclusion for optimal control problems of Mayer type and to develop Lagrangian and Hamiltonian necessary conditions I'm optimal control problems governed by nonconvex unbounded differential inclusions