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Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon

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  • Vincenzo Basco

    (The University of Melbourne)

Abstract

In the present paper, it is provided a representation result for the weak solutions of a class of evolutionary Hamilton–Jacobi–Bellman equations on infinite horizon, with Hamiltonians measurable in time and fiber convex. Such Hamiltonians are associated with a—faithful—representation, namely involving two functions measurable in time and locally Lipschitz in the state and control. Our results concern the recovering of a representation of convex Hamiltonians under a relaxed assumption on the Fenchel transform of the Hamiltonian with respect to the fiber. We apply them to investigate the uniqueness of weak solutions, vanishing at infinity, of a class of time-dependent Hamilton–Jacobi–Bellman equations. Assuming a viability condition on the domain of the aforementioned Fenchel transform, these weak solutions are regarded as an appropriate value function of an infinite horizon control problem under state constraints.

Suggested Citation

  • Vincenzo Basco, 2020. "Representation of Weak Solutions of Convex Hamilton–Jacobi–Bellman Equations on Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 370-390, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01763-1
    DOI: 10.1007/s10957-020-01763-1
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    References listed on IDEAS

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    1. R. T. Rockafellar, 1981. "Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 424-436, August.
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