This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functio...

A general SIR-model with vaccination and treatment is considered as a multi-input optimal control problem over a fixed time horizon. Existence and local optimality of singular controls is investigated. It is shown that the optimal vaccination schedule can be singular, but that treatment schedules are not.

Concept classes can canonically be represented by matrices with entries 1 and ?1. We use the singular value decomposition of this matrix to determine the optimal margins of embeddings of the concept classes of singletons and of half spaces in homogeneous Euclidean half spaces. For these concept classes the singular value decomposition can be used to construct optimal embeddings and also to prov...

Singular systems have been studied extensively during the last two decades due Abstract to their many practical applications. Such systems possess numerous properties not shared by the well-known state variable systems. This paper considers the linear tracking problem for the continuous-time singular systems. The Hamilton-Jacobi theory is used in order to compute the optimal control and associa...