Value Function of an Infinite Dimensional Infinite Horizon Problem
Résumé
We investigate the value function of an infinite horizon problem in the setting of an infinite-dimensional differential inclusion. In particular, we provide an upper estimate of its Gateaux subdifferential in terms of the Clarke subdifferen-tial of the integrand and the Clarke normal cone to the graph of the set-valued dynamics. We also derive a necessary optimality condition in the form of an Euler-Lagrange inclusion, the maximum principle and a sensitivity relation.
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