A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization

Alena Kopaničáková; Rolf Krause

doi:10.1007/978-3-030-95025-5_37

A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization

Alena Kopaničáková^*, Rolf Krause

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for unconstrained PDEs [2]. Their extension to constrained settings is not trivial as the coarse levels are often not capable of resolving the finest-level constraints sufficiently well, especially if the constraints are oscillatory [13]. The initial attempts to incorporate the constraints into the multilevel framework were associated with solving linear complementarity problems, see for instance [1, 5, 8, 14].

Original language	English (US)
Title of host publication	Domain Decomposition Methods in Science and Engineering XXVI
Editors	Susanne C. Brenner, Axel Klawonn, Jinchao Xu, Eric Chung, Jun Zou, Felix Kwok
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	355-363
Number of pages	9
ISBN (Print)	9783030950248
DOIs	https://doi.org/10.1007/978-3-030-95025-5_37
State	Published - 2022
Event	26th International Conference on Domain Decomposition Methods, 2020 - Virtual, Online Duration: Dec 7 2020 → Dec 12 2020

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	145
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	26th International Conference on Domain Decomposition Methods, 2020
City	Virtual, Online
Period	12/7/20 → 12/12/20

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

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10.1007/978-3-030-95025-5_37

Cite this

Kopaničáková, A., & Krause, R. (2022). A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization. In S. C. Brenner, A. Klawonn, J. Xu, E. Chung, J. Zou, & F. Kwok (Eds.), Domain Decomposition Methods in Science and Engineering XXVI (pp. 355-363). (Lecture Notes in Computational Science and Engineering; Vol. 145). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-95025-5_37

Kopaničáková, Alena ; Krause, Rolf. / A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization. Domain Decomposition Methods in Science and Engineering XXVI. editor / Susanne C. Brenner ; Axel Klawonn ; Jinchao Xu ; Eric Chung ; Jun Zou ; Felix Kwok. Springer Science and Business Media Deutschland GmbH, 2022. pp. 355-363 (Lecture Notes in Computational Science and Engineering).

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abstract = "Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for unconstrained PDEs [2]. Their extension to constrained settings is not trivial as the coarse levels are often not capable of resolving the finest-level constraints sufficiently well, especially if the constraints are oscillatory [13]. The initial attempts to incorporate the constraints into the multilevel framework were associated with solving linear complementarity problems, see for instance [1, 5, 8, 14].",

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Kopaničáková, A & Krause, R 2022, A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization. in SC Brenner, A Klawonn, J Xu, E Chung, J Zou & F Kwok (eds), Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol. 145, Springer Science and Business Media Deutschland GmbH, pp. 355-363, 26th International Conference on Domain Decomposition Methods, 2020, Virtual, Online, 12/7/20. https://doi.org/10.1007/978-3-030-95025-5_37

A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization. / Kopaničáková, Alena; Krause, Rolf.
Domain Decomposition Methods in Science and Engineering XXVI. ed. / Susanne C. Brenner; Axel Klawonn; Jinchao Xu; Eric Chung; Jun Zou; Felix Kwok. Springer Science and Business Media Deutschland GmbH, 2022. p. 355-363 (Lecture Notes in Computational Science and Engineering; Vol. 145).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their convergence rate is often independent of the problem size and the number of required arithmetic operations grows proportionally with the number of unknowns. These methods were originally designed for unconstrained PDEs [2]. Their extension to constrained settings is not trivial as the coarse levels are often not capable of resolving the finest-level constraints sufficiently well, especially if the constraints are oscillatory [13]. The initial attempts to incorporate the constraints into the multilevel framework were associated with solving linear complementarity problems, see for instance [1, 5, 8, 14].

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Kopaničáková A, Krause R. A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization. In Brenner SC, Klawonn A, Xu J, Chung E, Zou J, Kwok F, editors, Domain Decomposition Methods in Science and Engineering XXVI. Springer Science and Business Media Deutschland GmbH. 2022. p. 355-363. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-95025-5_37

A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization

Abstract

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Bibliographical note

ASJC Scopus subject areas

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