A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems

dc.citation.articleNumber62en_US
dc.citation.journalTitleESAIM: Control, Optimisation and Calculus of Variationsen_US
dc.citation.volumeNumber30en_US
dc.contributor.authorHeinkenschloss, Matthiasen_US
dc.contributor.authorKroeger, Nathaniel J.en_US
dc.date.accessioned2024-10-01T14:03:57Zen_US
dc.date.available2024-10-01T14:03:57Zen_US
dc.date.issued2024en_US
dc.description.abstractA new diagonalization technique for the parallel-in-time solution of linear-quadratic optimal control problems with time-invariant system matrices is introduced. The target problems are often derived from a semi-discretization of a Partial Differential Equation (PDE)-constrained optimization problem. The solution of large-scale time dependent optimal control problems is computationally challenging as the states, controls, and adjoints are coupled to each other throughout the whole time domain. This computational difficulty motivates the use of parallel-in-time methods. For time-periodic problems our diagonalization efficiently transforms the discretized optimality system into nt (=number of time steps) decoupled complex valued 2ny × 2ny systems, where ny is the dimension of the state space. These systems resemble optimality systems corresponding to a steady-state version of the optimal control problem and they can be solved in parallel across the time steps, but are complex valued. For optimal control problems with initial value state equations a direct solution via diagonalization is not possible, but an efficient preconditioner can be constructed from the corresponding time periodic optimal control problem. The preconditioner can be efficiently applied parallel-in-time using the diagonalization technique. The observed number of preconditioned GMRES iterations is small and insensitive to the size of the problem discretization.en_US
dc.identifier.citationHeinkenschloss, M., & Kroeger, N. J. (2024). A new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, 30, 62. https://doi.org/10.1051/cocv/2024051en_US
dc.identifier.digitalcocv220151en_US
dc.identifier.doihttps://doi.org/10.1051/cocv/2024051en_US
dc.identifier.urihttps://hdl.handle.net/1911/117896en_US
dc.language.isoengen_US
dc.publisherEDP Sciencesen_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleA new diagonalization based method for parallel-in-time solution of linear-quadratic optimal control problemsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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