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arXiv · 2305.02585

L$\infty$/L1 Duality Results In Optimal Control Problems

Dan Goreac·Alain Rapaport
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Abstract

We provide a duality result linking the value function for a control problem with supremum cost H under an isoperimetric inequality G $\le$ gmax, and the value function for the same controlled dynamics with cost G and state constraint H $\le$ hmax. This duality is proven for initial conditions at which lower semi-continuity of the value functions can be guaranteed, and is completed with optimality considerations. Furthermore, we provide structural assumptions on the dynamics under which such regularity can be established. As a by-product, we illustrate the partial equivalence between recentworks dealing with non-pharmaceutically controlled epidemics under peak or budget restrictions.

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Dan Goreac, Alain Rapaport. 2023-05-04. L$\infty$/L1 Duality Results In Optimal Control Problems. https://arxiv.org/abs/2305.02585

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