Epsilon-Maximum Principle of Pontryagin Type and Perturbation Analysis of Convex Optimal Control Problems

In this paper we study the first-order behaviour of the optimal-value function associated with a convex parametric problem of optimal control. A formula for the subdifferential of the optimal-value function is derived without assuming the existence of optimal solutions to the unperturbed problem. The so-called epsilon-maximum principle is a key ingredient in the writing of our main sensitivity result.