This paper investigates the value function, V , of a Mayer optimal control problem with the state equation given by a differential inclusion. First, we obtain an invariance property for the proximal and Fréchet subdifferentials of V along optimal trajectories. Then, we extend the analysis to the sub/superjets of V , obtaining new sensitivity relations of second order. By applying sensitivity an...

In 1977, Hedy Attouch established that a sequence of (closed proper) convex functions epi-converges to a convex function if and only if the graphs of the subdifferentials converge (in the Mosco sense) to the subdifferential of the limiting function and (roughly speaking) there is a condition that fixes the constant of integration. We show that the theorem is valid if instead one considers funct...