On the SQH scheme to solve non-smooth PDE optimal control problems
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- A sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints. The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin'sA sequential quadratic Hamiltonian (SQH) scheme for solving different classes of non-smooth and non-convex PDE optimal control problems is investigated considering seven different benchmark problems with increasing difficulty. These problems include linear and nonlinear PDEs with linear and bilinear control mechanisms, non-convex and discontinuous costs of the controls, L\(^1\) tracking terms, and the case of state constraints. The SQH method is based on the characterisation of optimality of PDE optimal control problems by the Pontryagin's maximum principle (PMP). For each problem, a theoretical discussion of the PMP optimality condition is given and results of numerical experiments are presented that demonstrate the large range of applicability of the SQH scheme.…
Autor(en): | Tim Breitenbach, Alfio Borzì |
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URN: | urn:nbn:de:bvb:20-opus-180936 |
Dokumentart: | Preprint (Vorabdruck) |
Institute der Universität: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Sprache der Veröffentlichung: | Englisch |
Titel des übergeordneten Werkes / der Zeitschrift (Englisch): | Numerical Functional Analysis and Optimization |
Erscheinungsjahr: | 2019 |
Originalveröffentlichung / Quelle: | Numerical Functional Analysis and Optimization 2019, 40:13, 1489-1531, DOI: 10.1080/01630563.2019.1599911 |
DOI: | https://doi.org/10.1080/01630563.2019.1599911 |
Allgemeine fachliche Zuordnung (DDC-Klassifikation): | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Freie Schlagwort(e): | Pontryagin maximum principle; SQH method; non-smooth optimization; nonconvex optimization |
Datum der Freischaltung: | 27.04.2020 |
Anmerkungen: | This is an Accepted Manuscript of an article published by Taylor & Francis in Numerical Functional Analysis and Optimization on 27.04.2019, available online: http://www.tandfonline.com/10.1080/01630563.2019.1599911. |
Lizenz (Deutsch): | Deutsches Urheberrecht |