research-article

Implicit-Explicit Runge--Kutta Schemes for Numerical Discretization of Optimal Control Problems

Authors:

S. SteffensenAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 51, Issue 4

Pages 1875 - 1899

https://doi.org/10.1137/120865045

Published: 01 January 2013 Publication History

Abstract

Implicit-explicit (IMEX) Runge--Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and nonstiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge--Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable transformations of the adjoint equation, order conditions up to order three are proven, and the relation between adjoint schemes obtained through different transformations is investigated as well. Conditions for the IMEX Runge--Kutta methods to be symplectic are also derived. A numerical example illustrating the theoretical properties is presented.

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Cited By

Lang JSchmitt B(2024)Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal ControlJournal of Optimization Theory and Applications10.1007/s10957-024-02541-z203:1(985-1026)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10957-024-02541-z
Wang HZhang QShu C(2019)Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion ProblemsJournal of Scientific Computing10.1007/s10915-019-01072-481:3(2080-2114)Online publication date: 1-Dec-2019
https://dl.acm.org/doi/10.1007/s10915-019-01072-4

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 51, Issue 4

2013

594 pages

ISSN:0036-1429

DOI:10.1137/sjnaam.51.4

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© 2013, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2013

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Cited By

Lang JSchmitt B(2024)Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal ControlJournal of Optimization Theory and Applications10.1007/s10957-024-02541-z203:1(985-1026)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1007/s10957-024-02541-z
Wang HZhang QShu C(2019)Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion ProblemsJournal of Scientific Computing10.1007/s10915-019-01072-481:3(2080-2114)Online publication date: 1-Dec-2019
https://dl.acm.org/doi/10.1007/s10915-019-01072-4

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