On singular control problems, the time-stretching method, and the weak-M1 topology
Optimization and Control
2020-10-28 v3 Probability
Abstract
We consider a general class of singular control problems with state constraints. Budhiraja and Ross (2006) established the existence of optimal controls for a relaxed version of this class of problems by using the so-called `time-stretching' method and the J1-topology. We show that the weak-M1 topology is better suited for establishing existence, since it allows to bypass the time-transformations, without any additional effort. Furthermore, we reveal how the time-scaling feature in the definition of the weak-M1 distance embeds the time-stretching method's scheme. This case study suggests that one can benefit from working with the weak-M1 topology in other singular control frameworks, such as queueing control problems under heavy traffic.
Keywords
Cite
@article{arxiv.1905.02608,
title = {On singular control problems, the time-stretching method, and the weak-M1 topology},
author = {Asaf Cohen},
journal= {arXiv preprint arXiv:1905.02608},
year = {2020}
}