Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems
For researchers in optimal control and numerical methods, this work identifies which linear multistep methods are suitable for adjoint equations, but the results are incremental as they extend known properties to a specific class of problems.
This paper investigates high-order linear multistep schemes for time discretization of adjoint equations in optimal control problems, finding that Adams-Moulton and Adams-Bashford methods lose accuracy while BDF methods preserve high-order accuracy, with extensions to hyperbolic relaxation systems.
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-Bashford 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.