L$\infty$/L1 Duality Results In Optimal Control Problems
Optimization and Control
2023-05-05 v1
Abstract
We provide a duality result linking the value function for a control problem with supremum cost H under an isoperimetric inequality G gmax, and the value function for the same controlled dynamics with cost G and state constraint H 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.
Keywords
Cite
@article{arxiv.2305.02585,
title = {L$\infty$/L1 Duality Results In Optimal Control Problems},
author = {Dan Goreac and Alain Rapaport},
journal= {arXiv preprint arXiv:2305.02585},
year = {2023}
}