Infinite Horizon Optimal Control of Non-Convex Problems under State Constraints

Hélène Frankowska (1)

1 IMJ - Institut de Mathématiques de Jussieu

We consider the undiscounted infinite horizon optimal control problem under state constraints in the absence of convexity/concavity assumptions. Then the value function is, in general, nonsmooth. Using the tools of set-valued and nonsmooth analysis, the necessary optimality conditions and sensitivity relations are derived in such a framework. We also investigate relaxation theorems and uniqueness of solutions of the Hamilton-Jacobi-Bellman equation arising in this setting.

Mots clés: sensitivity relations; maximum principle; Infinite horizon; value function; Hamilton-Jacobi-Bellman equation; relaxation theorem

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Hélène Frankowska. Infinite Horizon Optimal Control of Non-Convex Problems under State Constraints. Advances in Mathematical Economics, 23, Springer, 2020, Advances in Mathematical Economics, 978-981-15-0713-7. ⟨10.1007/978-981-15-0713-7_2⟩. ⟨hal-02325736⟩