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A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems

Authors:

Matthias Gerdts,

Martin KunkelAuthors Info & Claims

Computational Optimization and Applications, Volume 48, Issue 3

Pages 601 - 633

https://doi.org/10.1007/s10589-009-9275-0

Published: 01 April 2011 Publication History

Abstract

We investigate a semi-smooth Newton method for the numerical solution of optimal control problems subject to differential-algebraic equations (DAEs) and mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer-Burmeister function the local minimum principle is transformed into an equivalent nonlinear and semi-smooth equation in appropriate Banach spaces. This nonlinear and semi-smooth equation is solved by a semi-smooth Newton method. We extend known local and global convergence results for ODE optimal control problems to the DAE optimal control problems under consideration. Special emphasis is laid on the calculation of Newton steps which are given by a linear DAE boundary value problem. Regularity conditions which ensure the existence of solutions are provided. A regularization strategy for inconsistent boundary value problems is suggested. Numerical illustrations for the optimal control of a pendulum and for the optimal control of discretized Navier-Stokes equations conclude the article.

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Cited By

Chen JRabitz H(2019)On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic EquationsJournal of Optimization Theory and Applications10.1007/s10957-018-1364-8180:2(518-535)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s10957-018-1364-8
De Marchi AGerdts M(2019)Nonsmooth Newton’s Method: Some Structure ExploitationComputational Science – ICCS 201910.1007/978-3-030-22744-9_32(409-420)Online publication date: 12-Jun-2019
https://dl.acm.org/doi/10.1007/978-3-030-22744-9_32

A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems

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cover image Computational Optimization and Applications

Computational Optimization and Applications Volume 48, Issue 3

April 2011

316 pages

ISSN:0926-6003

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Copyright © Copyright © 2011 Springer Science+Business Media, LLC.

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Kluwer Academic Publishers

United States

Publication History

Published: 01 April 2011

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Cited By

Chen JRabitz H(2019)On Lifting Operators and Regularity of Nonsmooth Newton Methods for Optimal Control Problems of Differential Algebraic EquationsJournal of Optimization Theory and Applications10.1007/s10957-018-1364-8180:2(518-535)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.1007/s10957-018-1364-8
De Marchi AGerdts M(2019)Nonsmooth Newton’s Method: Some Structure ExploitationComputational Science – ICCS 201910.1007/978-3-030-22744-9_32(409-420)Online publication date: 12-Jun-2019
https://dl.acm.org/doi/10.1007/978-3-030-22744-9_32

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