TY - JOUR
T1 - Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems
AU - Albi, Giacomo
AU - Herty, Michael
AU - Pareschi, Lorenzo
PY - 2019/8/1
Y1 - 2019/8/1
N2 - 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.
AB - 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.
KW - Linear Multistep methods
KW - optimal control problems
KW - semi-lagrangian schemes
KW - hyperbolic relaxation systems
KW - conservation laws
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85062573891&partnerID=MN8TOARS
U2 - 10.1016/j.amc.2019.02.021
DO - 10.1016/j.amc.2019.02.021
M3 - Article
SN - 0096-3003
VL - 354
SP - 460
EP - 477
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -