550	RWTH Publication No: 811922        2018
TITLE	Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems
AUTHORS	Giacomo Albi, Michael Herty, Lorenzo Pareschi
ABSTRACT	We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for Adams–Moulton and Adams–Bashforth methods, whereas BDF methods preserve high-order accuracy. Subsequently we extend these results to semi-Lagrangian discretizations of hyperbolic relaxation systems. Computational results illustrate theoretical findings.
KEYWORDS	linear multistep methods, optimal control problems, semi–lagrangian schemes, hyperbolic relaxation systems, conservation laws
DOI	10.1016/j.amc.2019.02.021
PUBLICATION	Applied Mathematics and Computation, Vol. 354, 2019