Control problems with L1 perturbations and variational analysis in non-reflexive spaces

The value function plays an important role in optimization; it measures the sensitivity of the problem to perturbations of the objective function and the various constraints. Particularly interesting is the derivative of the value function, a measure of so called “differential stability”. When the value function is differentiable, it plays the role of a multiplier. In the context of dynamic optimization this observation establishes an heuristic relationship between the maximum principle and the dynamic programming approaches. Generally, however, the value function of a constrained optimization problem is far from being differentiable. To obtain a rigorous treatment of these heuristic relations one needs to apply the techniques of nonsmooth analysis