Optimality conditions for $\mathbb {L}^p$ problems with reflected dynamics
Volume 127 / 2024
Banach Center Publications 127 (2024), 89-107
MSC: Primary 49J45; Secondary 49N15, 90C46.
DOI: 10.4064/bc127-4
Abstract
We look into optimality considerations for control problems consisting in minimizing, for $p\in (1,\infty ]$, the $\mathbb {L}^{p}$ norms of a Borel measurable cost function, in finite time, and over all trajectories associated with a controlled dynamics which is reflected in a compact prox-regular set. This is done via the linear programming formulations of the problem inspired by the considerations in [Goreac et al., Journal of Differential Equations 290 (2021), 78–115]. The optimality conditions are given in terms of support of the optimal measures and the conditions echo the maximizers of Hamiltonians.
